(x-3)(x-3)=5+6(x-3)

Simple and best practice solution for (x-3)(x-3)=5+6(x-3) 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 (x-3)(x-3)=5+6(x-3) equation:


Simplifying
(x + -3)(x + -3) = 5 + 6(x + -3)

Reorder the terms:
(-3 + x)(x + -3) = 5 + 6(x + -3)

Reorder the terms:
(-3 + x)(-3 + x) = 5 + 6(x + -3)

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) = 5 + 6(x + -3)
((-3 * -3 + x * -3) + x(-3 + x)) = 5 + 6(x + -3)
((9 + -3x) + x(-3 + x)) = 5 + 6(x + -3)
(9 + -3x + (-3 * x + x * x)) = 5 + 6(x + -3)
(9 + -3x + (-3x + x2)) = 5 + 6(x + -3)

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) = 5 + 6(x + -3)

Reorder the terms:
9 + -6x + x2 = 5 + 6(-3 + x)
9 + -6x + x2 = 5 + (-3 * 6 + x * 6)
9 + -6x + x2 = 5 + (-18 + 6x)

Combine like terms: 5 + -18 = -13
9 + -6x + x2 = -13 + 6x

Solving
9 + -6x + x2 = -13 + 6x

Solving for variable 'x'.

Reorder the terms:
9 + 13 + -6x + -6x + x2 = -13 + 6x + 13 + -6x

Combine like terms: 9 + 13 = 22
22 + -6x + -6x + x2 = -13 + 6x + 13 + -6x

Combine like terms: -6x + -6x = -12x
22 + -12x + x2 = -13 + 6x + 13 + -6x

Reorder the terms:
22 + -12x + x2 = -13 + 13 + 6x + -6x

Combine like terms: -13 + 13 = 0
22 + -12x + x2 = 0 + 6x + -6x
22 + -12x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
22 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -12x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + -12x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -12x + x2 = 0 + -22
-12x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
-12x + x2 = -22

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -22 + 36

Reorder the terms:
36 + -12x + x2 = -22 + 36

Combine like terms: -22 + 36 = 14
36 + -12x + x2 = 14

Factor a perfect square on the left side:
(x + -6)(x + -6) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -6) equal to 3.741657387 and -3.741657387.

Subproblem 1

x + -6 = 3.741657387 Simplifying x + -6 = 3.741657387 Reorder the terms: -6 + x = 3.741657387 Solving -6 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3.741657387 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.741657387 + 6 x = 3.741657387 + 6 Combine like terms: 3.741657387 + 6 = 9.741657387 x = 9.741657387 Simplifying x = 9.741657387

Subproblem 2

x + -6 = -3.741657387 Simplifying x + -6 = -3.741657387 Reorder the terms: -6 + x = -3.741657387 Solving -6 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3.741657387 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.741657387 + 6 x = -3.741657387 + 6 Combine like terms: -3.741657387 + 6 = 2.258342613 x = 2.258342613 Simplifying x = 2.258342613

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.741657387, 2.258342613}

See similar equations:

| (3x^2)(5x^2+7x-10)= | | (x^2+4x+4)/(4x+8) | | x(2x^2+2)=65 | | b2/5 | | 4(2x-7)=26 | | x(2x^2+2x)=65 | | 4x+6=102-8x | | (z+4)+(z+1)+(z-1)+(z-1)=27 | | 7(t-4)+8t=5(3t+5)-9 | | -1x-1-8x-1-18=x | | 8x/-5+2x/-3 | | 6(3t-2)-5(2u+1)=27 | | -129-8x=7+21 | | -129-8x=-92-8x | | (x+36)/5=x | | 4(3z-7)+(5z+1)=56 | | x^2+4y^2-1=0 | | 8x-25=3+4x | | 6r-11=-11+8r | | 5(2y+3)+(5y-2)=84 | | x^2+3(y+3)= | | 5x-7+4x+70=180 | | 100-6x=8x+22 | | -1/6(x-12)+1/3(x+3)=x+13 | | 4+2i/2/3+1/2i | | (w-5)=36 | | x^2-11x-56=0 | | A+3=4(a+6) | | 4-(2-3x)=7-2(x-3) | | y=25.00+1.25(x-15) | | 7x-4+24=90 | | 7x+4+24=90 |

Equations solver categories