2x^2+22x-96=0

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Solution for 2x^2+22x-96=0 equation:


Simplifying
2x2 + 22x + -96 = 0

Reorder the terms:
-96 + 22x + 2x2 = 0

Solving
-96 + 22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 11x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-48 + 11x + x2)' equal to zero and attempt to solve: Simplifying -48 + 11x + x2 = 0 Solving -48 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 11x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 11x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 11x + x2 = 0 + 48 11x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 11x + x2 = 48 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 48 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 48 + 30.25 Combine like terms: 48 + 30.25 = 78.25 30.25 + 11x + x2 = 78.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + 5.5) equal to 8.845903006 and -8.845903006.

Subproblem 1

x + 5.5 = 8.845903006 Simplifying x + 5.5 = 8.845903006 Reorder the terms: 5.5 + x = 8.845903006 Solving 5.5 + x = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 8.845903006 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 8.845903006 + -5.5 x = 8.845903006 + -5.5 Combine like terms: 8.845903006 + -5.5 = 3.345903006 x = 3.345903006 Simplifying x = 3.345903006

Subproblem 2

x + 5.5 = -8.845903006 Simplifying x + 5.5 = -8.845903006 Reorder the terms: 5.5 + x = -8.845903006 Solving 5.5 + x = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -8.845903006 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -8.845903006 + -5.5 x = -8.845903006 + -5.5 Combine like terms: -8.845903006 + -5.5 = -14.345903006 x = -14.345903006 Simplifying x = -14.345903006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.345903006, -14.345903006}

Solution

x = {3.345903006, -14.345903006}

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