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Simplifying 2x2 + 2x + -11664 = 0 Reorder the terms: -11664 + 2x + 2x2 = 0 Solving -11664 + 2x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5832 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5832 + x + x2)' equal to zero and attempt to solve: Simplifying -5832 + x + x2 = 0 Solving -5832 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5832' to each side of the equation. -5832 + x + 5832 + x2 = 0 + 5832 Reorder the terms: -5832 + 5832 + x + x2 = 0 + 5832 Combine like terms: -5832 + 5832 = 0 0 + x + x2 = 0 + 5832 x + x2 = 0 + 5832 Combine like terms: 0 + 5832 = 5832 x + x2 = 5832 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 5832 + 0.25 Reorder the terms: 0.25 + x + x2 = 5832 + 0.25 Combine like terms: 5832 + 0.25 = 5832.25 0.25 + x + x2 = 5832.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5832.25 Calculate the square root of the right side: 76.369169172 Break this problem into two subproblems by setting (x + 0.5) equal to 76.369169172 and -76.369169172.Subproblem 1
x + 0.5 = 76.369169172 Simplifying x + 0.5 = 76.369169172 Reorder the terms: 0.5 + x = 76.369169172 Solving 0.5 + x = 76.369169172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 76.369169172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 76.369169172 + -0.5 x = 76.369169172 + -0.5 Combine like terms: 76.369169172 + -0.5 = 75.869169172 x = 75.869169172 Simplifying x = 75.869169172Subproblem 2
x + 0.5 = -76.369169172 Simplifying x + 0.5 = -76.369169172 Reorder the terms: 0.5 + x = -76.369169172 Solving 0.5 + x = -76.369169172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -76.369169172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -76.369169172 + -0.5 x = -76.369169172 + -0.5 Combine like terms: -76.369169172 + -0.5 = -76.869169172 x = -76.869169172 Simplifying x = -76.869169172Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.869169172, -76.869169172}Solution
x = {75.869169172, -76.869169172}
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