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Simplifying 8x2 + -5x + -120 = 0 Reorder the terms: -120 + -5x + 8x2 = 0 Solving -120 + -5x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15 + -0.625x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -0.625x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -0.625x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -0.625x + x2 = 0 + 15 -0.625x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -0.625x + x2 = 15 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 15 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 15 + 0.09765625 Combine like terms: 15 + 0.09765625 = 15.09765625 0.09765625 + -0.625x + x2 = 15.09765625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 15.09765625 Calculate the square root of the right side: 3.885570261 Break this problem into two subproblems by setting (x + -0.3125) equal to 3.885570261 and -3.885570261.Subproblem 1
x + -0.3125 = 3.885570261 Simplifying x + -0.3125 = 3.885570261 Reorder the terms: -0.3125 + x = 3.885570261 Solving -0.3125 + x = 3.885570261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 3.885570261 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 3.885570261 + 0.3125 x = 3.885570261 + 0.3125 Combine like terms: 3.885570261 + 0.3125 = 4.198070261 x = 4.198070261 Simplifying x = 4.198070261Subproblem 2
x + -0.3125 = -3.885570261 Simplifying x + -0.3125 = -3.885570261 Reorder the terms: -0.3125 + x = -3.885570261 Solving -0.3125 + x = -3.885570261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -3.885570261 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -3.885570261 + 0.3125 x = -3.885570261 + 0.3125 Combine like terms: -3.885570261 + 0.3125 = -3.573070261 x = -3.573070261 Simplifying x = -3.573070261Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.198070261, -3.573070261}
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