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Simplifying x = -0.4x2 + 80(50) + -1600 Multiply 80 * 50 x = -0.4x2 + 4000 + -1600 Reorder the terms: x = 4000 + -1600 + -0.4x2 Combine like terms: 4000 + -1600 = 2400 x = 2400 + -0.4x2 Solving x = 2400 + -0.4x2 Solving for variable 'x'. Reorder the terms: -2400 + x + 0.4x2 = 2400 + -0.4x2 + -2400 + 0.4x2 Reorder the terms: -2400 + x + 0.4x2 = 2400 + -2400 + -0.4x2 + 0.4x2 Combine like terms: 2400 + -2400 = 0 -2400 + x + 0.4x2 = 0 + -0.4x2 + 0.4x2 -2400 + x + 0.4x2 = -0.4x2 + 0.4x2 Combine like terms: -0.4x2 + 0.4x2 = 0.0 -2400 + x + 0.4x2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -6000 + 2.5x + x2 = 0 Move the constant term to the right: Add '6000' to each side of the equation. -6000 + 2.5x + 6000 + x2 = 0 + 6000 Reorder the terms: -6000 + 6000 + 2.5x + x2 = 0 + 6000 Combine like terms: -6000 + 6000 = 0 0 + 2.5x + x2 = 0 + 6000 2.5x + x2 = 0 + 6000 Combine like terms: 0 + 6000 = 6000 2.5x + x2 = 6000 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 2.5x + 0.25 + x2 = 6000 + 0.25 Reorder the terms: 0.25 + 2.5x + x2 = 6000 + 0.25 Combine like terms: 6000 + 0.25 = 6000.25 0.25 + 2.5x + x2 = 6000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6000.25 Calculate the square root of the right side: 77.46128065 Break this problem into two subproblems by setting (x + 0.5) equal to 77.46128065 and -77.46128065.Subproblem 1
x + 0.5 = 77.46128065 Simplifying x + 0.5 = 77.46128065 Reorder the terms: 0.5 + x = 77.46128065 Solving 0.5 + x = 77.46128065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 77.46128065 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 77.46128065 + -0.5 x = 77.46128065 + -0.5 Combine like terms: 77.46128065 + -0.5 = 76.96128065 x = 76.96128065 Simplifying x = 76.96128065Subproblem 2
x + 0.5 = -77.46128065 Simplifying x + 0.5 = -77.46128065 Reorder the terms: 0.5 + x = -77.46128065 Solving 0.5 + x = -77.46128065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -77.46128065 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -77.46128065 + -0.5 x = -77.46128065 + -0.5 Combine like terms: -77.46128065 + -0.5 = -77.96128065 x = -77.96128065 Simplifying x = -77.96128065Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.96128065, -77.96128065}
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