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Simplifying 167.5 = -4x2 + 80x + -150 Reorder the terms: 167.5 = -150 + 80x + -4x2 Solving 167.5 = -150 + 80x + -4x2 Solving for variable 'x'. Combine like terms: 167.5 + 150 = 317.5 317.5 + -80x + 4x2 = -150 + 80x + -4x2 + 150 + -80x + 4x2 Reorder the terms: 317.5 + -80x + 4x2 = -150 + 150 + 80x + -80x + -4x2 + 4x2 Combine like terms: -150 + 150 = 0 317.5 + -80x + 4x2 = 0 + 80x + -80x + -4x2 + 4x2 317.5 + -80x + 4x2 = 80x + -80x + -4x2 + 4x2 Combine like terms: 80x + -80x = 0 317.5 + -80x + 4x2 = 0 + -4x2 + 4x2 317.5 + -80x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 317.5 + -80x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 79.375 + -20x + x2 = 0 Move the constant term to the right: Add '-79.375' to each side of the equation. 79.375 + -20x + -79.375 + x2 = 0 + -79.375 Reorder the terms: 79.375 + -79.375 + -20x + x2 = 0 + -79.375 Combine like terms: 79.375 + -79.375 = 0.000 0.000 + -20x + x2 = 0 + -79.375 -20x + x2 = 0 + -79.375 Combine like terms: 0 + -79.375 = -79.375 -20x + x2 = -79.375 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -79.375 + 100 Reorder the terms: 100 + -20x + x2 = -79.375 + 100 Combine like terms: -79.375 + 100 = 20.625 100 + -20x + x2 = 20.625 Factor a perfect square on the left side: (x + -10)(x + -10) = 20.625 Calculate the square root of the right side: 4.541475531 Break this problem into two subproblems by setting (x + -10) equal to 4.541475531 and -4.541475531.Subproblem 1
x + -10 = 4.541475531 Simplifying x + -10 = 4.541475531 Reorder the terms: -10 + x = 4.541475531 Solving -10 + x = 4.541475531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 4.541475531 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4.541475531 + 10 x = 4.541475531 + 10 Combine like terms: 4.541475531 + 10 = 14.541475531 x = 14.541475531 Simplifying x = 14.541475531Subproblem 2
x + -10 = -4.541475531 Simplifying x + -10 = -4.541475531 Reorder the terms: -10 + x = -4.541475531 Solving -10 + x = -4.541475531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -4.541475531 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4.541475531 + 10 x = -4.541475531 + 10 Combine like terms: -4.541475531 + 10 = 5.458524469 x = 5.458524469 Simplifying x = 5.458524469Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.541475531, 5.458524469}
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