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Simplifying -5x2 + -39x + -8 = 0 Reorder the terms: -8 + -39x + -5x2 = 0 Solving -8 + -39x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 39x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 39x + 5x2)' equal to zero and attempt to solve: Simplifying 8 + 39x + 5x2 = 0 Solving 8 + 39x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + 7.8x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 7.8x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + 7.8x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 7.8x + x2 = 0 + -1.6 7.8x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 7.8x + x2 = -1.6 The x term is 7.8x. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8x + 15.21 + x2 = -1.6 + 15.21 Reorder the terms: 15.21 + 7.8x + x2 = -1.6 + 15.21 Combine like terms: -1.6 + 15.21 = 13.61 15.21 + 7.8x + x2 = 13.61 Factor a perfect square on the left side: (x + 3.9)(x + 3.9) = 13.61 Calculate the square root of the right side: 3.689173349 Break this problem into two subproblems by setting (x + 3.9) equal to 3.689173349 and -3.689173349.Subproblem 1
x + 3.9 = 3.689173349 Simplifying x + 3.9 = 3.689173349 Reorder the terms: 3.9 + x = 3.689173349 Solving 3.9 + x = 3.689173349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = 3.689173349 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = 3.689173349 + -3.9 x = 3.689173349 + -3.9 Combine like terms: 3.689173349 + -3.9 = -0.210826651 x = -0.210826651 Simplifying x = -0.210826651Subproblem 2
x + 3.9 = -3.689173349 Simplifying x + 3.9 = -3.689173349 Reorder the terms: 3.9 + x = -3.689173349 Solving 3.9 + x = -3.689173349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = -3.689173349 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = -3.689173349 + -3.9 x = -3.689173349 + -3.9 Combine like terms: -3.689173349 + -3.9 = -7.589173349 x = -7.589173349 Simplifying x = -7.589173349Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.210826651, -7.589173349}Solution
x = {-0.210826651, -7.589173349}
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