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Simplifying 4x2 + 8x + 4 = -60x + -22 Reorder the terms: 4 + 8x + 4x2 = -60x + -22 Reorder the terms: 4 + 8x + 4x2 = -22 + -60x Solving 4 + 8x + 4x2 = -22 + -60x Solving for variable 'x'. Reorder the terms: 4 + 22 + 8x + 60x + 4x2 = -22 + -60x + 22 + 60x Combine like terms: 4 + 22 = 26 26 + 8x + 60x + 4x2 = -22 + -60x + 22 + 60x Combine like terms: 8x + 60x = 68x 26 + 68x + 4x2 = -22 + -60x + 22 + 60x Reorder the terms: 26 + 68x + 4x2 = -22 + 22 + -60x + 60x Combine like terms: -22 + 22 = 0 26 + 68x + 4x2 = 0 + -60x + 60x 26 + 68x + 4x2 = -60x + 60x Combine like terms: -60x + 60x = 0 26 + 68x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + 34x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + 34x + 2x2)' equal to zero and attempt to solve: Simplifying 13 + 34x + 2x2 = 0 Solving 13 + 34x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + 17x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + 17x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + 17x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + 17x + x2 = 0 + -6.5 17x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 17x + x2 = -6.5 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -6.5 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -6.5 + 72.25 Combine like terms: -6.5 + 72.25 = 65.75 72.25 + 17x + x2 = 65.75 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 65.75 Calculate the square root of the right side: 8.10863737 Break this problem into two subproblems by setting (x + 8.5) equal to 8.10863737 and -8.10863737.Subproblem 1
x + 8.5 = 8.10863737 Simplifying x + 8.5 = 8.10863737 Reorder the terms: 8.5 + x = 8.10863737 Solving 8.5 + x = 8.10863737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 8.10863737 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.10863737 + -8.5 x = 8.10863737 + -8.5 Combine like terms: 8.10863737 + -8.5 = -0.39136263 x = -0.39136263 Simplifying x = -0.39136263Subproblem 2
x + 8.5 = -8.10863737 Simplifying x + 8.5 = -8.10863737 Reorder the terms: 8.5 + x = -8.10863737 Solving 8.5 + x = -8.10863737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -8.10863737 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.10863737 + -8.5 x = -8.10863737 + -8.5 Combine like terms: -8.10863737 + -8.5 = -16.60863737 x = -16.60863737 Simplifying x = -16.60863737Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.39136263, -16.60863737}Solution
x = {-0.39136263, -16.60863737}
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