3(x-2)(x-2)=(13-7x)(13-7x)

Simple and best practice solution for 3(x-2)(x-2)=(13-7x)(13-7x) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 3(x-2)(x-2)=(13-7x)(13-7x) equation:


Simplifying
3(x + -2)(x + -2) = (13 + -7x)(13 + -7x)

Reorder the terms:
3(-2 + x)(x + -2) = (13 + -7x)(13 + -7x)

Reorder the terms:
3(-2 + x)(-2 + x) = (13 + -7x)(13 + -7x)

Multiply (-2 + x) * (-2 + x)
3(-2(-2 + x) + x(-2 + x)) = (13 + -7x)(13 + -7x)
3((-2 * -2 + x * -2) + x(-2 + x)) = (13 + -7x)(13 + -7x)
3((4 + -2x) + x(-2 + x)) = (13 + -7x)(13 + -7x)
3(4 + -2x + (-2 * x + x * x)) = (13 + -7x)(13 + -7x)
3(4 + -2x + (-2x + x2)) = (13 + -7x)(13 + -7x)

Combine like terms: -2x + -2x = -4x
3(4 + -4x + x2) = (13 + -7x)(13 + -7x)
(4 * 3 + -4x * 3 + x2 * 3) = (13 + -7x)(13 + -7x)
(12 + -12x + 3x2) = (13 + -7x)(13 + -7x)

Multiply (13 + -7x) * (13 + -7x)
12 + -12x + 3x2 = (13(13 + -7x) + -7x * (13 + -7x))
12 + -12x + 3x2 = ((13 * 13 + -7x * 13) + -7x * (13 + -7x))
12 + -12x + 3x2 = ((169 + -91x) + -7x * (13 + -7x))
12 + -12x + 3x2 = (169 + -91x + (13 * -7x + -7x * -7x))
12 + -12x + 3x2 = (169 + -91x + (-91x + 49x2))

Combine like terms: -91x + -91x = -182x
12 + -12x + 3x2 = (169 + -182x + 49x2)

Solving
12 + -12x + 3x2 = 169 + -182x + 49x2

Solving for variable 'x'.

Reorder the terms:
12 + -169 + -12x + 182x + 3x2 + -49x2 = 169 + -182x + 49x2 + -169 + 182x + -49x2

Combine like terms: 12 + -169 = -157
-157 + -12x + 182x + 3x2 + -49x2 = 169 + -182x + 49x2 + -169 + 182x + -49x2

Combine like terms: -12x + 182x = 170x
-157 + 170x + 3x2 + -49x2 = 169 + -182x + 49x2 + -169 + 182x + -49x2

Combine like terms: 3x2 + -49x2 = -46x2
-157 + 170x + -46x2 = 169 + -182x + 49x2 + -169 + 182x + -49x2

Reorder the terms:
-157 + 170x + -46x2 = 169 + -169 + -182x + 182x + 49x2 + -49x2

Combine like terms: 169 + -169 = 0
-157 + 170x + -46x2 = 0 + -182x + 182x + 49x2 + -49x2
-157 + 170x + -46x2 = -182x + 182x + 49x2 + -49x2

Combine like terms: -182x + 182x = 0
-157 + 170x + -46x2 = 0 + 49x2 + -49x2
-157 + 170x + -46x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
-157 + 170x + -46x2 = 0

Begin completing the square.  Divide all terms by
-46 the coefficient of the squared term: 

Divide each side by '-46'.
3.413043478 + -3.695652174x + x2 = 0

Move the constant term to the right:

Add '-3.413043478' to each side of the equation.
3.413043478 + -3.695652174x + -3.413043478 + x2 = 0 + -3.413043478

Reorder the terms:
3.413043478 + -3.413043478 + -3.695652174x + x2 = 0 + -3.413043478

Combine like terms: 3.413043478 + -3.413043478 = 0.000000000
0.000000000 + -3.695652174x + x2 = 0 + -3.413043478
-3.695652174x + x2 = 0 + -3.413043478

Combine like terms: 0 + -3.413043478 = -3.413043478
-3.695652174x + x2 = -3.413043478

The x term is -3.695652174x.  Take half its coefficient (-1.847826087).
Square it (3.414461248) and add it to both sides.

Add '3.414461248' to each side of the equation.
-3.695652174x + 3.414461248 + x2 = -3.413043478 + 3.414461248

Reorder the terms:
3.414461248 + -3.695652174x + x2 = -3.413043478 + 3.414461248

Combine like terms: -3.413043478 + 3.414461248 = 0.00141777
3.414461248 + -3.695652174x + x2 = 0.00141777

Factor a perfect square on the left side:
(x + -1.847826087)(x + -1.847826087) = 0.00141777

Calculate the square root of the right side: 0.037653287

Break this problem into two subproblems by setting 
(x + -1.847826087) equal to 0.037653287 and -0.037653287.

Subproblem 1

x + -1.847826087 = 0.037653287 Simplifying x + -1.847826087 = 0.037653287 Reorder the terms: -1.847826087 + x = 0.037653287 Solving -1.847826087 + x = 0.037653287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.847826087' to each side of the equation. -1.847826087 + 1.847826087 + x = 0.037653287 + 1.847826087 Combine like terms: -1.847826087 + 1.847826087 = 0.000000000 0.000000000 + x = 0.037653287 + 1.847826087 x = 0.037653287 + 1.847826087 Combine like terms: 0.037653287 + 1.847826087 = 1.885479374 x = 1.885479374 Simplifying x = 1.885479374

Subproblem 2

x + -1.847826087 = -0.037653287 Simplifying x + -1.847826087 = -0.037653287 Reorder the terms: -1.847826087 + x = -0.037653287 Solving -1.847826087 + x = -0.037653287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.847826087' to each side of the equation. -1.847826087 + 1.847826087 + x = -0.037653287 + 1.847826087 Combine like terms: -1.847826087 + 1.847826087 = 0.000000000 0.000000000 + x = -0.037653287 + 1.847826087 x = -0.037653287 + 1.847826087 Combine like terms: -0.037653287 + 1.847826087 = 1.8101728 x = 1.8101728 Simplifying x = 1.8101728

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.885479374, 1.8101728}

See similar equations:

| 18+8x=32 | | 6a^2b/2ab^3 | | 18u^6-16u^3/2u^3 | | (X+3)4=29 | | n=(7+11) | | x^4-3x^3-2x^2+10x-12=0 | | cos(5x)+cos(x)-cos(3x)=0 | | n^6-n^5=7n^3-7n^4 | | x^2+5=-17 | | (a/b)^3(2b/3a)^4 | | (2m+1)x+m^2+m=0 | | 3x-y+2z=14 | | 7=z+3 | | z^2+2-42=0 | | y^2-12y+8= | | 4x-2(x-2)-8=0 | | 5x+3y=82 | | 2-x=4-x^2 | | 90*10x-20= | | ((x*0.10)(0.2)+(x*0.10))+78=x | | 7*6-3+5=26 | | 1/3(18-6x | | x^3+x^2*y=180 | | B^2+5b-35=36 | | Cosx=6/15 | | ((x*0.07)(0.2)+(x*0.07))+78=x | | x^3+x^2+y=180 | | 14n^2+19n=-6 | | ((x*0.09)(0.2)+(x*0.09))+78=x | | ((x*0.06)(0.2)+(x*0.06))+78=x | | ((x*0.08)(0.2)+(x*0.08))+78=x | | (5+4x)(5+4x)=0 |

Equations solver categories