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Simplifying 0 = -0.04x2 + 0.25x + 33.59 Reorder the terms: 0 = 33.59 + 0.25x + -0.04x2 Solving 0 = 33.59 + 0.25x + -0.04x2 Solving for variable 'x'. Combine like terms: 0 + -33.59 = -33.59 -33.59 + -0.25x + 0.04x2 = 33.59 + 0.25x + -0.04x2 + -33.59 + -0.25x + 0.04x2 Reorder the terms: -33.59 + -0.25x + 0.04x2 = 33.59 + -33.59 + 0.25x + -0.25x + -0.04x2 + 0.04x2 Combine like terms: 33.59 + -33.59 = 0.00 -33.59 + -0.25x + 0.04x2 = 0.00 + 0.25x + -0.25x + -0.04x2 + 0.04x2 -33.59 + -0.25x + 0.04x2 = 0.25x + -0.25x + -0.04x2 + 0.04x2 Combine like terms: 0.25x + -0.25x = 0.00 -33.59 + -0.25x + 0.04x2 = 0.00 + -0.04x2 + 0.04x2 -33.59 + -0.25x + 0.04x2 = -0.04x2 + 0.04x2 Combine like terms: -0.04x2 + 0.04x2 = 0.00 -33.59 + -0.25x + 0.04x2 = 0.00 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -839.75 + -6.25x + x2 = 0 Move the constant term to the right: Add '839.75' to each side of the equation. -839.75 + -6.25x + 839.75 + x2 = 0 + 839.75 Reorder the terms: -839.75 + 839.75 + -6.25x + x2 = 0 + 839.75 Combine like terms: -839.75 + 839.75 = 0.00 0.00 + -6.25x + x2 = 0 + 839.75 -6.25x + x2 = 0 + 839.75 Combine like terms: 0 + 839.75 = 839.75 -6.25x + x2 = 839.75 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 839.75 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 839.75 + 9.765625 Combine like terms: 839.75 + 9.765625 = 849.515625 9.765625 + -6.25x + x2 = 849.515625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 849.515625 Calculate the square root of the right side: 29.146451328 Break this problem into two subproblems by setting (x + -3.125) equal to 29.146451328 and -29.146451328.Subproblem 1
x + -3.125 = 29.146451328 Simplifying x + -3.125 = 29.146451328 Reorder the terms: -3.125 + x = 29.146451328 Solving -3.125 + x = 29.146451328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 29.146451328 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 29.146451328 + 3.125 x = 29.146451328 + 3.125 Combine like terms: 29.146451328 + 3.125 = 32.271451328 x = 32.271451328 Simplifying x = 32.271451328Subproblem 2
x + -3.125 = -29.146451328 Simplifying x + -3.125 = -29.146451328 Reorder the terms: -3.125 + x = -29.146451328 Solving -3.125 + x = -29.146451328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -29.146451328 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -29.146451328 + 3.125 x = -29.146451328 + 3.125 Combine like terms: -29.146451328 + 3.125 = -26.021451328 x = -26.021451328 Simplifying x = -26.021451328Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.271451328, -26.021451328}
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