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Simplifying 50 = -16x2 + 80x + 5 Reorder the terms: 50 = 5 + 80x + -16x2 Solving 50 = 5 + 80x + -16x2 Solving for variable 'x'. Combine like terms: 50 + -5 = 45 45 + -80x + 16x2 = 5 + 80x + -16x2 + -5 + -80x + 16x2 Reorder the terms: 45 + -80x + 16x2 = 5 + -5 + 80x + -80x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 45 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2 45 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2 Combine like terms: 80x + -80x = 0 45 + -80x + 16x2 = 0 + -16x2 + 16x2 45 + -80x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 45 + -80x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.8125 + -5x + x2 = 0 Move the constant term to the right: Add '-2.8125' to each side of the equation. 2.8125 + -5x + -2.8125 + x2 = 0 + -2.8125 Reorder the terms: 2.8125 + -2.8125 + -5x + x2 = 0 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + -5x + x2 = 0 + -2.8125 -5x + x2 = 0 + -2.8125 Combine like terms: 0 + -2.8125 = -2.8125 -5x + x2 = -2.8125 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -2.8125 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2.8125 + 6.25 Combine like terms: -2.8125 + 6.25 = 3.4375 6.25 + -5x + x2 = 3.4375 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3.4375 Calculate the square root of the right side: 1.854049622 Break this problem into two subproblems by setting (x + -2.5) equal to 1.854049622 and -1.854049622.Subproblem 1
x + -2.5 = 1.854049622 Simplifying x + -2.5 = 1.854049622 Reorder the terms: -2.5 + x = 1.854049622 Solving -2.5 + x = 1.854049622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.854049622 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.854049622 + 2.5 x = 1.854049622 + 2.5 Combine like terms: 1.854049622 + 2.5 = 4.354049622 x = 4.354049622 Simplifying x = 4.354049622Subproblem 2
x + -2.5 = -1.854049622 Simplifying x + -2.5 = -1.854049622 Reorder the terms: -2.5 + x = -1.854049622 Solving -2.5 + x = -1.854049622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.854049622 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.854049622 + 2.5 x = -1.854049622 + 2.5 Combine like terms: -1.854049622 + 2.5 = 0.645950378 x = 0.645950378 Simplifying x = 0.645950378Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.354049622, 0.645950378}
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