X^2+5X=315

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Solution for X^2+5X=315 equation:


Simplifying
X2 + 5X = 315

Reorder the terms:
5X + X2 = 315

Solving
5X + X2 = 315

Solving for variable 'X'.

Reorder the terms:
-315 + 5X + X2 = 315 + -315

Combine like terms: 315 + -315 = 0
-315 + 5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '315' to each side of the equation.
-315 + 5X + 315 + X2 = 0 + 315

Reorder the terms:
-315 + 315 + 5X + X2 = 0 + 315

Combine like terms: -315 + 315 = 0
0 + 5X + X2 = 0 + 315
5X + X2 = 0 + 315

Combine like terms: 0 + 315 = 315
5X + X2 = 315

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 = 315 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 315 + 6.25

Combine like terms: 315 + 6.25 = 321.25
6.25 + 5X + X2 = 321.25

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 321.25

Calculate the square root of the right side: 17.923448329

Break this problem into two subproblems by setting 
(X + 2.5) equal to 17.923448329 and -17.923448329.

Subproblem 1

X + 2.5 = 17.923448329 Simplifying X + 2.5 = 17.923448329 Reorder the terms: 2.5 + X = 17.923448329 Solving 2.5 + X = 17.923448329 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 = 17.923448329 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 17.923448329 + -2.5 X = 17.923448329 + -2.5 Combine like terms: 17.923448329 + -2.5 = 15.423448329 X = 15.423448329 Simplifying X = 15.423448329

Subproblem 2

X + 2.5 = -17.923448329 Simplifying X + 2.5 = -17.923448329 Reorder the terms: 2.5 + X = -17.923448329 Solving 2.5 + X = -17.923448329 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 = -17.923448329 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -17.923448329 + -2.5 X = -17.923448329 + -2.5 Combine like terms: -17.923448329 + -2.5 = -20.423448329 X = -20.423448329 Simplifying X = -20.423448329

Solution

The solution to the problem is based on the solutions from the subproblems. X = {15.423448329, -20.423448329}

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