(8x-3)(8x-3)=30

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Solution for (8x-3)(8x-3)=30 equation:


Simplifying
(8x + -3)(8x + -3) = 30

Reorder the terms:
(-3 + 8x)(8x + -3) = 30

Reorder the terms:
(-3 + 8x)(-3 + 8x) = 30

Multiply (-3 + 8x) * (-3 + 8x)
(-3(-3 + 8x) + 8x * (-3 + 8x)) = 30
((-3 * -3 + 8x * -3) + 8x * (-3 + 8x)) = 30
((9 + -24x) + 8x * (-3 + 8x)) = 30
(9 + -24x + (-3 * 8x + 8x * 8x)) = 30
(9 + -24x + (-24x + 64x2)) = 30

Combine like terms: -24x + -24x = -48x
(9 + -48x + 64x2) = 30

Solving
9 + -48x + 64x2 = 30

Solving for variable 'x'.

Reorder the terms:
9 + -30 + -48x + 64x2 = 30 + -30

Combine like terms: 9 + -30 = -21
-21 + -48x + 64x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-21 + -48x + 64x2 = 0

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

Divide each side by '64'.
-0.328125 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.328125' to each side of the equation.
-0.328125 + -0.75x + 0.328125 + x2 = 0 + 0.328125

Reorder the terms:
-0.328125 + 0.328125 + -0.75x + x2 = 0 + 0.328125

Combine like terms: -0.328125 + 0.328125 = 0.000000
0.000000 + -0.75x + x2 = 0 + 0.328125
-0.75x + x2 = 0 + 0.328125

Combine like terms: 0 + 0.328125 = 0.328125
-0.75x + x2 = 0.328125

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.328125 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.328125 + 0.140625

Combine like terms: 0.328125 + 0.140625 = 0.46875
0.140625 + -0.75x + x2 = 0.46875

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.46875

Calculate the square root of the right side: 0.684653197

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.684653197 and -0.684653197.

Subproblem 1

x + -0.375 = 0.684653197 Simplifying x + -0.375 = 0.684653197 Reorder the terms: -0.375 + x = 0.684653197 Solving -0.375 + x = 0.684653197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.684653197 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.684653197 + 0.375 x = 0.684653197 + 0.375 Combine like terms: 0.684653197 + 0.375 = 1.059653197 x = 1.059653197 Simplifying x = 1.059653197

Subproblem 2

x + -0.375 = -0.684653197 Simplifying x + -0.375 = -0.684653197 Reorder the terms: -0.375 + x = -0.684653197 Solving -0.375 + x = -0.684653197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.684653197 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.684653197 + 0.375 x = -0.684653197 + 0.375 Combine like terms: -0.684653197 + 0.375 = -0.309653197 x = -0.309653197 Simplifying x = -0.309653197

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.059653197, -0.309653197}

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