15x+(x^2)=64

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Solution for 15x+(x^2)=64 equation:


Simplifying
15x + (x2) = 64
15x + x2 = 64

Solving
15x + x2 = 64

Solving for variable 'x'.

Reorder the terms:
-64 + 15x + x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 15x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + 15x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 15x + x2 = 0 + 64
15x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
15x + x2 = 64

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 64 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 64 + 56.25

Combine like terms: 64 + 56.25 = 120.25
56.25 + 15x + x2 = 120.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(x + 7.5) equal to 10.9658561 and -10.9658561.

Subproblem 1

x + 7.5 = 10.9658561 Simplifying x + 7.5 = 10.9658561 Reorder the terms: 7.5 + x = 10.9658561 Solving 7.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 10.9658561 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.9658561 + -7.5 x = 10.9658561 + -7.5 Combine like terms: 10.9658561 + -7.5 = 3.4658561 x = 3.4658561 Simplifying x = 3.4658561

Subproblem 2

x + 7.5 = -10.9658561 Simplifying x + 7.5 = -10.9658561 Reorder the terms: 7.5 + x = -10.9658561 Solving 7.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -10.9658561 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.9658561 + -7.5 x = -10.9658561 + -7.5 Combine like terms: -10.9658561 + -7.5 = -18.4658561 x = -18.4658561 Simplifying x = -18.4658561

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.4658561, -18.4658561}

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