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Simplifying 32x + -0.8x2 = 160 Solving 32x + -0.8x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + 32x + -0.8x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 32x + -0.8x2 = 0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 200 + -40x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -40x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -40x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -40x + x2 = 0 + -200 -40x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -40x + x2 = -200 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -200 + 400 Reorder the terms: 400 + -40x + x2 = -200 + 400 Combine like terms: -200 + 400 = 200 400 + -40x + x2 = 200 Factor a perfect square on the left side: (x + -20)(x + -20) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -20) equal to 14.142135624 and -14.142135624.Subproblem 1
x + -20 = 14.142135624 Simplifying x + -20 = 14.142135624 Reorder the terms: -20 + x = 14.142135624 Solving -20 + x = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 14.142135624 + 20 Combine like terms: -20 + 20 = 0 0 + x = 14.142135624 + 20 x = 14.142135624 + 20 Combine like terms: 14.142135624 + 20 = 34.142135624 x = 34.142135624 Simplifying x = 34.142135624Subproblem 2
x + -20 = -14.142135624 Simplifying x + -20 = -14.142135624 Reorder the terms: -20 + x = -14.142135624 Solving -20 + x = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -14.142135624 + 20 Combine like terms: -20 + 20 = 0 0 + x = -14.142135624 + 20 x = -14.142135624 + 20 Combine like terms: -14.142135624 + 20 = 5.857864376 x = 5.857864376 Simplifying x = 5.857864376Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.142135624, 5.857864376}
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