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Simplifying -5x2 + -41x + -48 = 0 Reorder the terms: -48 + -41x + -5x2 = 0 Solving -48 + -41x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(48 + 41x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(48 + 41x + 5x2)' equal to zero and attempt to solve: Simplifying 48 + 41x + 5x2 = 0 Solving 48 + 41x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 9.6 + 8.2x + x2 = 0 Move the constant term to the right: Add '-9.6' to each side of the equation. 9.6 + 8.2x + -9.6 + x2 = 0 + -9.6 Reorder the terms: 9.6 + -9.6 + 8.2x + x2 = 0 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + 8.2x + x2 = 0 + -9.6 8.2x + x2 = 0 + -9.6 Combine like terms: 0 + -9.6 = -9.6 8.2x + x2 = -9.6 The x term is 8.2x. Take half its coefficient (4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. 8.2x + 16.81 + x2 = -9.6 + 16.81 Reorder the terms: 16.81 + 8.2x + x2 = -9.6 + 16.81 Combine like terms: -9.6 + 16.81 = 7.21 16.81 + 8.2x + x2 = 7.21 Factor a perfect square on the left side: (x + 4.1)(x + 4.1) = 7.21 Calculate the square root of the right side: 2.685144316 Break this problem into two subproblems by setting (x + 4.1) equal to 2.685144316 and -2.685144316.Subproblem 1
x + 4.1 = 2.685144316 Simplifying x + 4.1 = 2.685144316 Reorder the terms: 4.1 + x = 2.685144316 Solving 4.1 + x = 2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = 2.685144316 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = 2.685144316 + -4.1 x = 2.685144316 + -4.1 Combine like terms: 2.685144316 + -4.1 = -1.414855684 x = -1.414855684 Simplifying x = -1.414855684Subproblem 2
x + 4.1 = -2.685144316 Simplifying x + 4.1 = -2.685144316 Reorder the terms: 4.1 + x = -2.685144316 Solving 4.1 + x = -2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = -2.685144316 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = -2.685144316 + -4.1 x = -2.685144316 + -4.1 Combine like terms: -2.685144316 + -4.1 = -6.785144316 x = -6.785144316 Simplifying x = -6.785144316Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.414855684, -6.785144316}Solution
x = {-1.414855684, -6.785144316}
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