=2x^2+11x+14

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Solution for =2x^2+11x+14 equation:


Simplifying
0 = 2x2 + 11x + 14

Reorder the terms:
0 = 14 + 11x + 2x2

Solving
0 = 14 + 11x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -14 = -14
-14 + -11x + -2x2 = 14 + 11x + 2x2 + -14 + -11x + -2x2

Reorder the terms:
-14 + -11x + -2x2 = 14 + -14 + 11x + -11x + 2x2 + -2x2

Combine like terms: 14 + -14 = 0
-14 + -11x + -2x2 = 0 + 11x + -11x + 2x2 + -2x2
-14 + -11x + -2x2 = 11x + -11x + 2x2 + -2x2

Combine like terms: 11x + -11x = 0
-14 + -11x + -2x2 = 0 + 2x2 + -2x2
-14 + -11x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-14 + -11x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 11x + 2x2) = 0

Factor a trinomial.
-1((7 + 2x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {-3.5, -2}

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