X^2+2.5X=114

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Solution for X^2+2.5X=114 equation:


Simplifying
X2 + 2.5X = 114

Reorder the terms:
2.5X + X2 = 114

Solving
2.5X + X2 = 114

Solving for variable 'X'.

Reorder the terms:
-114 + 2.5X + X2 = 114 + -114

Combine like terms: 114 + -114 = 0
-114 + 2.5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '114' to each side of the equation.
-114 + 2.5X + 114 + X2 = 0 + 114

Reorder the terms:
-114 + 114 + 2.5X + X2 = 0 + 114

Combine like terms: -114 + 114 = 0
0 + 2.5X + X2 = 0 + 114
2.5X + X2 = 0 + 114

Combine like terms: 0 + 114 = 114
2.5X + X2 = 114

The X term is 2.5X.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5X + 1.5625 + X2 = 114 + 1.5625

Reorder the terms:
1.5625 + 2.5X + X2 = 114 + 1.5625

Combine like terms: 114 + 1.5625 = 115.5625
1.5625 + 2.5X + X2 = 115.5625

Factor a perfect square on the left side:
(X + 1.25)(X + 1.25) = 115.5625

Calculate the square root of the right side: 10.75

Break this problem into two subproblems by setting 
(X + 1.25) equal to 10.75 and -10.75.

Subproblem 1

X + 1.25 = 10.75 Simplifying X + 1.25 = 10.75 Reorder the terms: 1.25 + X = 10.75 Solving 1.25 + X = 10.75 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = 10.75 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = 10.75 + -1.25 X = 10.75 + -1.25 Combine like terms: 10.75 + -1.25 = 9.5 X = 9.5 Simplifying X = 9.5

Subproblem 2

X + 1.25 = -10.75 Simplifying X + 1.25 = -10.75 Reorder the terms: 1.25 + X = -10.75 Solving 1.25 + X = -10.75 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = -10.75 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = -10.75 + -1.25 X = -10.75 + -1.25 Combine like terms: -10.75 + -1.25 = -12 X = -12 Simplifying X = -12

Solution

The solution to the problem is based on the solutions from the subproblems. X = {9.5, -12}

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