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Simplifying 34 = -16x2 + 80x + 5 Reorder the terms: 34 = 5 + 80x + -16x2 Solving 34 = 5 + 80x + -16x2 Solving for variable 'x'. Combine like terms: 34 + -5 = 29 29 + -80x + 16x2 = 5 + 80x + -16x2 + -5 + -80x + 16x2 Reorder the terms: 29 + -80x + 16x2 = 5 + -5 + 80x + -80x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 29 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2 29 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2 Combine like terms: 80x + -80x = 0 29 + -80x + 16x2 = 0 + -16x2 + 16x2 29 + -80x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 29 + -80x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.8125 + -5x + x2 = 0 Move the constant term to the right: Add '-1.8125' to each side of the equation. 1.8125 + -5x + -1.8125 + x2 = 0 + -1.8125 Reorder the terms: 1.8125 + -1.8125 + -5x + x2 = 0 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + -5x + x2 = 0 + -1.8125 -5x + x2 = 0 + -1.8125 Combine like terms: 0 + -1.8125 = -1.8125 -5x + x2 = -1.8125 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 = -1.8125 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.8125 + 6.25 Combine like terms: -1.8125 + 6.25 = 4.4375 6.25 + -5x + x2 = 4.4375 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.4375 Calculate the square root of the right side: 2.106537443 Break this problem into two subproblems by setting (x + -2.5) equal to 2.106537443 and -2.106537443.Subproblem 1
x + -2.5 = 2.106537443 Simplifying x + -2.5 = 2.106537443 Reorder the terms: -2.5 + x = 2.106537443 Solving -2.5 + x = 2.106537443 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 = 2.106537443 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.106537443 + 2.5 x = 2.106537443 + 2.5 Combine like terms: 2.106537443 + 2.5 = 4.606537443 x = 4.606537443 Simplifying x = 4.606537443Subproblem 2
x + -2.5 = -2.106537443 Simplifying x + -2.5 = -2.106537443 Reorder the terms: -2.5 + x = -2.106537443 Solving -2.5 + x = -2.106537443 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 = -2.106537443 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.106537443 + 2.5 x = -2.106537443 + 2.5 Combine like terms: -2.106537443 + 2.5 = 0.393462557 x = 0.393462557 Simplifying x = 0.393462557Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.606537443, 0.393462557}
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