(7x-1.5)(7x-9.5)+(4x+2)(4x+1)=0

Simple and best practice solution for (7x-1.5)(7x-9.5)+(4x+2)(4x+1)=0 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 (7x-1.5)(7x-9.5)+(4x+2)(4x+1)=0 equation:


Simplifying
(7x + -1.5)(7x + -9.5) + (4x + 2)(4x + 1) = 0

Reorder the terms:
(-1.5 + 7x)(7x + -9.5) + (4x + 2)(4x + 1) = 0

Reorder the terms:
(-1.5 + 7x)(-9.5 + 7x) + (4x + 2)(4x + 1) = 0

Multiply (-1.5 + 7x) * (-9.5 + 7x)
(-1.5(-9.5 + 7x) + 7x * (-9.5 + 7x)) + (4x + 2)(4x + 1) = 0
((-9.5 * -1.5 + 7x * -1.5) + 7x * (-9.5 + 7x)) + (4x + 2)(4x + 1) = 0
((14.25 + -10.5x) + 7x * (-9.5 + 7x)) + (4x + 2)(4x + 1) = 0
(14.25 + -10.5x + (-9.5 * 7x + 7x * 7x)) + (4x + 2)(4x + 1) = 0
(14.25 + -10.5x + (-66.5x + 49x2)) + (4x + 2)(4x + 1) = 0

Combine like terms: -10.5x + -66.5x = -77x
(14.25 + -77x + 49x2) + (4x + 2)(4x + 1) = 0

Reorder the terms:
14.25 + -77x + 49x2 + (2 + 4x)(4x + 1) = 0

Reorder the terms:
14.25 + -77x + 49x2 + (2 + 4x)(1 + 4x) = 0

Multiply (2 + 4x) * (1 + 4x)
14.25 + -77x + 49x2 + (2(1 + 4x) + 4x * (1 + 4x)) = 0
14.25 + -77x + 49x2 + ((1 * 2 + 4x * 2) + 4x * (1 + 4x)) = 0
14.25 + -77x + 49x2 + ((2 + 8x) + 4x * (1 + 4x)) = 0
14.25 + -77x + 49x2 + (2 + 8x + (1 * 4x + 4x * 4x)) = 0
14.25 + -77x + 49x2 + (2 + 8x + (4x + 16x2)) = 0

Combine like terms: 8x + 4x = 12x
14.25 + -77x + 49x2 + (2 + 12x + 16x2) = 0

Reorder the terms:
14.25 + 2 + -77x + 12x + 49x2 + 16x2 = 0

Combine like terms: 14.25 + 2 = 16.25
16.25 + -77x + 12x + 49x2 + 16x2 = 0

Combine like terms: -77x + 12x = -65x
16.25 + -65x + 49x2 + 16x2 = 0

Combine like terms: 49x2 + 16x2 = 65x2
16.25 + -65x + 65x2 = 0

Solving
16.25 + -65x + 65x2 = 0

Solving for variable 'x'.

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

Divide each side by '65'.
0.25 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1x + x2 = 0 + -0.25
-1x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1x + x2 = -0.25

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.25 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -1x + x2 = 0.00

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.00 and 0.00.

Subproblem 1

x + -0.5 = 0.00 Simplifying x + -0.5 = 0.00 Reorder the terms: -0.5 + x = 0.00 Solving -0.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.00 + 0.5 x = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 x = 0.5 Simplifying x = 0.5

Subproblem 2

x + -0.5 = 0.00 Simplifying x + -0.5 = 0.00 Reorder the terms: -0.5 + x = 0.00 Solving -0.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.00 + 0.5 x = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 x = 0.5 Simplifying x = 0.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5, 0.5}

See similar equations:

| 2-4(2-2x)=0 | | 5/x-16=38 | | 2n-(-7)=10 | | 29+17+90+x+y=180 | | (2x-15)=50+x | | 3x-7x+4=5x-7+2x | | 16x^2-3x^3-5x=0 | | 20-x^2=11 | | -12a/100x3=8 | | 255/68 | | 4x^3+x^2-15x-6=0 | | 17*5*3/68 | | ax+4=y | | X/(5x-1)=(3,2)/(14,4) | | 5x(6-6x)=49 | | 0.7x=x | | X/5x-1=3,2/14,4 | | secx=4cosx | | 6y-19=-7 | | 16x^3+7x^2+3x=415 | | 5u=8u-63 | | 3f+9f=60 | | -2(r+5)-3=5 | | 5(s+11)=35 | | (w+6)(w+1)=0 | | 17*2x=1-2x | | 2r^2-6r+12-4R= | | (3-5s)(-3+5s)=0 | | 7r^3-35r^2+6r-30= | | X+5=3-10 | | 44-y=25-2(8-3y)0 | | 2m^3+4m^2+6m+-2= |

Equations solver categories