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Simplifying -16x2 + 40x + 80 = 104.6 Reorder the terms: 80 + 40x + -16x2 = 104.6 Solving 80 + 40x + -16x2 = 104.6 Solving for variable 'x'. Reorder the terms: 80 + -104.6 + 40x + -16x2 = 104.6 + -104.6 Combine like terms: 80 + -104.6 = -24.6 -24.6 + 40x + -16x2 = 104.6 + -104.6 Combine like terms: 104.6 + -104.6 = 0.0 -24.6 + 40x + -16x2 = 0.0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.5375 + -2.5x + x2 = 0.0 Move the constant term to the right: Add '-1.5375' to each side of the equation. 1.5375 + -2.5x + -1.5375 + x2 = 0.0 + -1.5375 Reorder the terms: 1.5375 + -1.5375 + -2.5x + x2 = 0.0 + -1.5375 Combine like terms: 1.5375 + -1.5375 = 0.0000 0.0000 + -2.5x + x2 = 0.0 + -1.5375 -2.5x + x2 = 0.0 + -1.5375 Combine like terms: 0.0 + -1.5375 = -1.5375 -2.5x + x2 = -1.5375 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -1.5375 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.5375 + 1.5625 Combine like terms: -1.5375 + 1.5625 = 0.025 1.5625 + -2.5x + x2 = 0.025 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.025 Calculate the square root of the right side: 0.158113883 Break this problem into two subproblems by setting (x + -1.25) equal to 0.158113883 and -0.158113883.Subproblem 1
x + -1.25 = 0.158113883 Simplifying x + -1.25 = 0.158113883 Reorder the terms: -1.25 + x = 0.158113883 Solving -1.25 + x = 0.158113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.158113883 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.158113883 + 1.25 x = 0.158113883 + 1.25 Combine like terms: 0.158113883 + 1.25 = 1.408113883 x = 1.408113883 Simplifying x = 1.408113883Subproblem 2
x + -1.25 = -0.158113883 Simplifying x + -1.25 = -0.158113883 Reorder the terms: -1.25 + x = -0.158113883 Solving -1.25 + x = -0.158113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.158113883 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.158113883 + 1.25 x = -0.158113883 + 1.25 Combine like terms: -0.158113883 + 1.25 = 1.091886117 x = 1.091886117 Simplifying x = 1.091886117Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.408113883, 1.091886117}
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