x^2+5x-472=0

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Solution for x^2+5x-472=0 equation:


Simplifying
x2 + 5x + -472 = 0

Reorder the terms:
-472 + 5x + x2 = 0

Solving
-472 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '472' to each side of the equation.
-472 + 5x + 472 + x2 = 0 + 472

Reorder the terms:
-472 + 472 + 5x + x2 = 0 + 472

Combine like terms: -472 + 472 = 0
0 + 5x + x2 = 0 + 472
5x + x2 = 0 + 472

Combine like terms: 0 + 472 = 472
5x + x2 = 472

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 472 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 472 + 6.25

Combine like terms: 472 + 6.25 = 478.25
6.25 + 5x + x2 = 478.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 478.25

Calculate the square root of the right side: 21.868927729

Break this problem into two subproblems by setting 
(x + 2.5) equal to 21.868927729 and -21.868927729.

Subproblem 1

x + 2.5 = 21.868927729 Simplifying x + 2.5 = 21.868927729 Reorder the terms: 2.5 + x = 21.868927729 Solving 2.5 + x = 21.868927729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 21.868927729 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 21.868927729 + -2.5 x = 21.868927729 + -2.5 Combine like terms: 21.868927729 + -2.5 = 19.368927729 x = 19.368927729 Simplifying x = 19.368927729

Subproblem 2

x + 2.5 = -21.868927729 Simplifying x + 2.5 = -21.868927729 Reorder the terms: 2.5 + x = -21.868927729 Solving 2.5 + x = -21.868927729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -21.868927729 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -21.868927729 + -2.5 x = -21.868927729 + -2.5 Combine like terms: -21.868927729 + -2.5 = -24.368927729 x = -24.368927729 Simplifying x = -24.368927729

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.368927729, -24.368927729}

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