X^2+7X+10=140

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Solution for X^2+7X+10=140 equation:


Simplifying
X2 + 7X + 10 = 140

Reorder the terms:
10 + 7X + X2 = 140

Solving
10 + 7X + X2 = 140

Solving for variable 'X'.

Reorder the terms:
10 + -140 + 7X + X2 = 140 + -140

Combine like terms: 10 + -140 = -130
-130 + 7X + X2 = 140 + -140

Combine like terms: 140 + -140 = 0
-130 + 7X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + 7X + 130 + X2 = 0 + 130

Reorder the terms:
-130 + 130 + 7X + X2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + 7X + X2 = 0 + 130
7X + X2 = 0 + 130

Combine like terms: 0 + 130 = 130
7X + X2 = 130

The X term is 7X.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7X + 12.25 + X2 = 130 + 12.25

Reorder the terms:
12.25 + 7X + X2 = 130 + 12.25

Combine like terms: 130 + 12.25 = 142.25
12.25 + 7X + X2 = 142.25

Factor a perfect square on the left side:
(X + 3.5)(X + 3.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(X + 3.5) equal to 11.926860442 and -11.926860442.

Subproblem 1

X + 3.5 = 11.926860442 Simplifying X + 3.5 = 11.926860442 Reorder the terms: 3.5 + X = 11.926860442 Solving 3.5 + X = 11.926860442 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = 11.926860442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = 11.926860442 + -3.5 X = 11.926860442 + -3.5 Combine like terms: 11.926860442 + -3.5 = 8.426860442 X = 8.426860442 Simplifying X = 8.426860442

Subproblem 2

X + 3.5 = -11.926860442 Simplifying X + 3.5 = -11.926860442 Reorder the terms: 3.5 + X = -11.926860442 Solving 3.5 + X = -11.926860442 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = -11.926860442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = -11.926860442 + -3.5 X = -11.926860442 + -3.5 Combine like terms: -11.926860442 + -3.5 = -15.426860442 X = -15.426860442 Simplifying X = -15.426860442

Solution

The solution to the problem is based on the solutions from the subproblems. X = {8.426860442, -15.426860442}

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