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Simplifying 2x2 + 6x + -118 = 0 Reorder the terms: -118 + 6x + 2x2 = 0 Solving -118 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-59 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-59 + 3x + x2)' equal to zero and attempt to solve: Simplifying -59 + 3x + x2 = 0 Solving -59 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 3x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + 3x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 3x + x2 = 0 + 59 3x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 3x + x2 = 59 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 59 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 59 + 2.25 Combine like terms: 59 + 2.25 = 61.25 2.25 + 3x + x2 = 61.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + 1.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + 1.5 = 7.826237921 Simplifying x + 1.5 = 7.826237921 Reorder the terms: 1.5 + x = 7.826237921 Solving 1.5 + x = 7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.826237921 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.826237921 + -1.5 x = 7.826237921 + -1.5 Combine like terms: 7.826237921 + -1.5 = 6.326237921 x = 6.326237921 Simplifying x = 6.326237921Subproblem 2
x + 1.5 = -7.826237921 Simplifying x + 1.5 = -7.826237921 Reorder the terms: 1.5 + x = -7.826237921 Solving 1.5 + x = -7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.826237921 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.826237921 + -1.5 x = -7.826237921 + -1.5 Combine like terms: -7.826237921 + -1.5 = -9.326237921 x = -9.326237921 Simplifying x = -9.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.326237921, -9.326237921}Solution
x = {6.326237921, -9.326237921}
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