x^2-14x-40=

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Solution for x^2-14x-40= equation:


Simplifying
x2 + -14x + -40 = 0

Reorder the terms:
-40 + -14x + x2 = 0

Solving
-40 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -14x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -14x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -14x + x2 = 0 + 40
-14x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-14x + x2 = 40

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 40 + 49

Reorder the terms:
49 + -14x + x2 = 40 + 49

Combine like terms: 40 + 49 = 89
49 + -14x + x2 = 89

Factor a perfect square on the left side:
(x + -7)(x + -7) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + -7) equal to 9.433981132 and -9.433981132.

Subproblem 1

x + -7 = 9.433981132 Simplifying x + -7 = 9.433981132 Reorder the terms: -7 + x = 9.433981132 Solving -7 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 9.433981132 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.433981132 + 7 x = 9.433981132 + 7 Combine like terms: 9.433981132 + 7 = 16.433981132 x = 16.433981132 Simplifying x = 16.433981132

Subproblem 2

x + -7 = -9.433981132 Simplifying x + -7 = -9.433981132 Reorder the terms: -7 + x = -9.433981132 Solving -7 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -9.433981132 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.433981132 + 7 x = -9.433981132 + 7 Combine like terms: -9.433981132 + 7 = -2.433981132 x = -2.433981132 Simplifying x = -2.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.433981132, -2.433981132}

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