x^2+63x-160=0

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Solution for x^2+63x-160=0 equation:


Simplifying
x2 + 63x + -160 = 0

Reorder the terms:
-160 + 63x + x2 = 0

Solving
-160 + 63x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 63x + 160 + x2 = 0 + 160

Reorder the terms:
-160 + 160 + 63x + x2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + 63x + x2 = 0 + 160
63x + x2 = 0 + 160

Combine like terms: 0 + 160 = 160
63x + x2 = 160

The x term is 63x.  Take half its coefficient (31.5).
Square it (992.25) and add it to both sides.

Add '992.25' to each side of the equation.
63x + 992.25 + x2 = 160 + 992.25

Reorder the terms:
992.25 + 63x + x2 = 160 + 992.25

Combine like terms: 160 + 992.25 = 1152.25
992.25 + 63x + x2 = 1152.25

Factor a perfect square on the left side:
(x + 31.5)(x + 31.5) = 1152.25

Calculate the square root of the right side: 33.944808145

Break this problem into two subproblems by setting 
(x + 31.5) equal to 33.944808145 and -33.944808145.

Subproblem 1

x + 31.5 = 33.944808145 Simplifying x + 31.5 = 33.944808145 Reorder the terms: 31.5 + x = 33.944808145 Solving 31.5 + x = 33.944808145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 33.944808145 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 33.944808145 + -31.5 x = 33.944808145 + -31.5 Combine like terms: 33.944808145 + -31.5 = 2.444808145 x = 2.444808145 Simplifying x = 2.444808145

Subproblem 2

x + 31.5 = -33.944808145 Simplifying x + 31.5 = -33.944808145 Reorder the terms: 31.5 + x = -33.944808145 Solving 31.5 + x = -33.944808145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -33.944808145 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -33.944808145 + -31.5 x = -33.944808145 + -31.5 Combine like terms: -33.944808145 + -31.5 = -65.444808145 x = -65.444808145 Simplifying x = -65.444808145

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.444808145, -65.444808145}

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