0=x^2+14x+120

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Solution for 0=x^2+14x+120 equation:


Simplifying
0 = x2 + 14x + 120

Reorder the terms:
0 = 120 + 14x + x2

Solving
0 = 120 + 14x + x2

Solving for variable 'x'.

Combine like terms: 0 + -120 = -120
-120 + -14x + -1x2 = 120 + 14x + x2 + -120 + -14x + -1x2

Reorder the terms:
-120 + -14x + -1x2 = 120 + -120 + 14x + -14x + x2 + -1x2

Combine like terms: 120 + -120 = 0
-120 + -14x + -1x2 = 0 + 14x + -14x + x2 + -1x2
-120 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
-120 + -14x + -1x2 = 0 + x2 + -1x2
-120 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-120 + -14x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(120 + 14x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(120 + 14x + x2)' equal to zero and attempt to solve: Simplifying 120 + 14x + x2 = 0 Solving 120 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + 14x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + 14x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 14x + x2 = 0 + -120 14x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 14x + x2 = -120 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 = -120 + 49 Reorder the terms: 49 + 14x + x2 = -120 + 49 Combine like terms: -120 + 49 = -71 49 + 14x + x2 = -71 Factor a perfect square on the left side: (x + 7)(x + 7) = -71 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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