x^2+57x-630=0

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Solution for x^2+57x-630=0 equation:


Simplifying
x2 + 57x + -630 = 0

Reorder the terms:
-630 + 57x + x2 = 0

Solving
-630 + 57x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '630' to each side of the equation.
-630 + 57x + 630 + x2 = 0 + 630

Reorder the terms:
-630 + 630 + 57x + x2 = 0 + 630

Combine like terms: -630 + 630 = 0
0 + 57x + x2 = 0 + 630
57x + x2 = 0 + 630

Combine like terms: 0 + 630 = 630
57x + x2 = 630

The x term is 57x.  Take half its coefficient (28.5).
Square it (812.25) and add it to both sides.

Add '812.25' to each side of the equation.
57x + 812.25 + x2 = 630 + 812.25

Reorder the terms:
812.25 + 57x + x2 = 630 + 812.25

Combine like terms: 630 + 812.25 = 1442.25
812.25 + 57x + x2 = 1442.25

Factor a perfect square on the left side:
(x + 28.5)(x + 28.5) = 1442.25

Calculate the square root of the right side: 37.976966704

Break this problem into two subproblems by setting 
(x + 28.5) equal to 37.976966704 and -37.976966704.

Subproblem 1

x + 28.5 = 37.976966704 Simplifying x + 28.5 = 37.976966704 Reorder the terms: 28.5 + x = 37.976966704 Solving 28.5 + x = 37.976966704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28.5' to each side of the equation. 28.5 + -28.5 + x = 37.976966704 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + x = 37.976966704 + -28.5 x = 37.976966704 + -28.5 Combine like terms: 37.976966704 + -28.5 = 9.476966704 x = 9.476966704 Simplifying x = 9.476966704

Subproblem 2

x + 28.5 = -37.976966704 Simplifying x + 28.5 = -37.976966704 Reorder the terms: 28.5 + x = -37.976966704 Solving 28.5 + x = -37.976966704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28.5' to each side of the equation. 28.5 + -28.5 + x = -37.976966704 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + x = -37.976966704 + -28.5 x = -37.976966704 + -28.5 Combine like terms: -37.976966704 + -28.5 = -66.476966704 x = -66.476966704 Simplifying x = -66.476966704

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.476966704, -66.476966704}

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