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Simplifying -120 = -5x2 + -8x Reorder the terms: -120 = -8x + -5x2 Solving -120 = -8x + -5x2 Solving for variable 'x'. Reorder the terms: -120 + 8x + 5x2 = -8x + 8x + -5x2 + 5x2 Combine like terms: -8x + 8x = 0 -120 + 8x + 5x2 = 0 + -5x2 + 5x2 -120 + 8x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -120 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -24 + 1.6x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 1.6x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 1.6x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 1.6x + x2 = 0 + 24 1.6x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 1.6x + x2 = 24 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 24 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 24 + 0.64 Combine like terms: 24 + 0.64 = 24.64 0.64 + 1.6x + x2 = 24.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 24.64 Calculate the square root of the right side: 4.963869458 Break this problem into two subproblems by setting (x + 0.8) equal to 4.963869458 and -4.963869458.Subproblem 1
x + 0.8 = 4.963869458 Simplifying x + 0.8 = 4.963869458 Reorder the terms: 0.8 + x = 4.963869458 Solving 0.8 + x = 4.963869458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 4.963869458 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 4.963869458 + -0.8 x = 4.963869458 + -0.8 Combine like terms: 4.963869458 + -0.8 = 4.163869458 x = 4.163869458 Simplifying x = 4.163869458Subproblem 2
x + 0.8 = -4.963869458 Simplifying x + 0.8 = -4.963869458 Reorder the terms: 0.8 + x = -4.963869458 Solving 0.8 + x = -4.963869458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -4.963869458 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -4.963869458 + -0.8 x = -4.963869458 + -0.8 Combine like terms: -4.963869458 + -0.8 = -5.763869458 x = -5.763869458 Simplifying x = -5.763869458Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.163869458, -5.763869458}
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