(x)(x+5)=310

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Solution for (x)(x+5)=310 equation:


Simplifying
(x)(x + 5) = 310

Reorder the terms:
x(5 + x) = 310
(5 * x + x * x) = 310
(5x + x2) = 310

Solving
5x + x2 = 310

Solving for variable 'x'.

Reorder the terms:
-310 + 5x + x2 = 310 + -310

Combine like terms: 310 + -310 = 0
-310 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '310' to each side of the equation.
-310 + 5x + 310 + x2 = 0 + 310

Reorder the terms:
-310 + 310 + 5x + x2 = 0 + 310

Combine like terms: -310 + 310 = 0
0 + 5x + x2 = 0 + 310
5x + x2 = 0 + 310

Combine like terms: 0 + 310 = 310
5x + x2 = 310

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 = 310 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 310 + 6.25

Combine like terms: 310 + 6.25 = 316.25
6.25 + 5x + x2 = 316.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 316.25

Calculate the square root of the right side: 17.783419244

Break this problem into two subproblems by setting 
(x + 2.5) equal to 17.783419244 and -17.783419244.

Subproblem 1

x + 2.5 = 17.783419244 Simplifying x + 2.5 = 17.783419244 Reorder the terms: 2.5 + x = 17.783419244 Solving 2.5 + x = 17.783419244 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 = 17.783419244 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 17.783419244 + -2.5 x = 17.783419244 + -2.5 Combine like terms: 17.783419244 + -2.5 = 15.283419244 x = 15.283419244 Simplifying x = 15.283419244

Subproblem 2

x + 2.5 = -17.783419244 Simplifying x + 2.5 = -17.783419244 Reorder the terms: 2.5 + x = -17.783419244 Solving 2.5 + x = -17.783419244 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 = -17.783419244 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -17.783419244 + -2.5 x = -17.783419244 + -2.5 Combine like terms: -17.783419244 + -2.5 = -20.283419244 x = -20.283419244 Simplifying x = -20.283419244

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.283419244, -20.283419244}

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