64x^2=48x+9

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Solution for 64x^2=48x+9 equation:


Simplifying
64x2 = 48x + 9

Reorder the terms:
64x2 = 9 + 48x

Solving
64x2 = 9 + 48x

Solving for variable 'x'.

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

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

Combine like terms: 9 + -9 = 0
-9 + -48x + 64x2 = 0 + 48x + -48x
-9 + -48x + 64x2 = 48x + -48x

Combine like terms: 48x + -48x = 0
-9 + -48x + 64x2 = 0

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

Divide each side by '64'.
-0.140625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.140625' to each side of the equation.
-0.140625 + -0.75x + 0.140625 + x2 = 0 + 0.140625

Reorder the terms:
-0.140625 + 0.140625 + -0.75x + x2 = 0 + 0.140625

Combine like terms: -0.140625 + 0.140625 = 0.000000
0.000000 + -0.75x + x2 = 0 + 0.140625
-0.75x + x2 = 0 + 0.140625

Combine like terms: 0 + 0.140625 = 0.140625
-0.75x + x2 = 0.140625

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 = 0.140625 + 0.140625

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

Combine like terms: 0.140625 + 0.140625 = 0.28125
0.140625 + -0.75x + x2 = 0.28125

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.28125

Calculate the square root of the right side: 0.530330086

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.530330086 and -0.530330086.

Subproblem 1

x + -0.375 = 0.530330086 Simplifying x + -0.375 = 0.530330086 Reorder the terms: -0.375 + x = 0.530330086 Solving -0.375 + x = 0.530330086 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 = 0.530330086 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.530330086 + 0.375 x = 0.530330086 + 0.375 Combine like terms: 0.530330086 + 0.375 = 0.905330086 x = 0.905330086 Simplifying x = 0.905330086

Subproblem 2

x + -0.375 = -0.530330086 Simplifying x + -0.375 = -0.530330086 Reorder the terms: -0.375 + x = -0.530330086 Solving -0.375 + x = -0.530330086 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 = -0.530330086 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.530330086 + 0.375 x = -0.530330086 + 0.375 Combine like terms: -0.530330086 + 0.375 = -0.155330086 x = -0.155330086 Simplifying x = -0.155330086

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.905330086, -0.155330086}

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