5x^2=64-x

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Solution for 5x^2=64-x equation:


Simplifying
5x2 = 64 + -1x

Solving
5x2 = 64 + -1x

Solving for variable 'x'.

Reorder the terms:
-64 + x + 5x2 = 64 + -1x + -64 + x

Reorder the terms:
-64 + x + 5x2 = 64 + -64 + -1x + x

Combine like terms: 64 + -64 = 0
-64 + x + 5x2 = 0 + -1x + x
-64 + x + 5x2 = -1x + x

Combine like terms: -1x + x = 0
-64 + x + 5x2 = 0

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

Divide each side by '5'.
-12.8 + 0.2x + x2 = 0

Move the constant term to the right:

Add '12.8' to each side of the equation.
-12.8 + 0.2x + 12.8 + x2 = 0 + 12.8

Reorder the terms:
-12.8 + 12.8 + 0.2x + x2 = 0 + 12.8

Combine like terms: -12.8 + 12.8 = 0.0
0.0 + 0.2x + x2 = 0 + 12.8
0.2x + x2 = 0 + 12.8

Combine like terms: 0 + 12.8 = 12.8
0.2x + x2 = 12.8

The x term is x.  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.
0.2x + 0.25 + x2 = 12.8 + 0.25

Reorder the terms:
0.25 + 0.2x + x2 = 12.8 + 0.25

Combine like terms: 12.8 + 0.25 = 13.05
0.25 + 0.2x + x2 = 13.05

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 13.05

Calculate the square root of the right side: 3.612478374

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.612478374 and -3.612478374.

Subproblem 1

x + 0.5 = 3.612478374 Simplifying x + 0.5 = 3.612478374 Reorder the terms: 0.5 + x = 3.612478374 Solving 0.5 + x = 3.612478374 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 = 3.612478374 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.612478374 + -0.5 x = 3.612478374 + -0.5 Combine like terms: 3.612478374 + -0.5 = 3.112478374 x = 3.112478374 Simplifying x = 3.112478374

Subproblem 2

x + 0.5 = -3.612478374 Simplifying x + 0.5 = -3.612478374 Reorder the terms: 0.5 + x = -3.612478374 Solving 0.5 + x = -3.612478374 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 = -3.612478374 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.612478374 + -0.5 x = -3.612478374 + -0.5 Combine like terms: -3.612478374 + -0.5 = -4.112478374 x = -4.112478374 Simplifying x = -4.112478374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.112478374, -4.112478374}

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