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Simplifying 0 = -0.025x2 + x + 6 Reorder the terms: 0 = 6 + x + -0.025x2 Solving 0 = 6 + x + -0.025x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -1x + 0.025x2 = 6 + x + -0.025x2 + -6 + -1x + 0.025x2 Reorder the terms: -6 + -1x + 0.025x2 = 6 + -6 + x + -1x + -0.025x2 + 0.025x2 Combine like terms: 6 + -6 = 0 -6 + -1x + 0.025x2 = 0 + x + -1x + -0.025x2 + 0.025x2 -6 + -1x + 0.025x2 = x + -1x + -0.025x2 + 0.025x2 Combine like terms: x + -1x = 0 -6 + -1x + 0.025x2 = 0 + -0.025x2 + 0.025x2 -6 + -1x + 0.025x2 = -0.025x2 + 0.025x2 Combine like terms: -0.025x2 + 0.025x2 = 0.000 -6 + -1x + 0.025x2 = 0.000 Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. -240 + -40x + x2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + -40x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -40x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -40x + x2 = 0 + 240 -40x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -40x + x2 = 240 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 = 240 + 400 Reorder the terms: 400 + -40x + x2 = 240 + 400 Combine like terms: 240 + 400 = 640 400 + -40x + x2 = 640 Factor a perfect square on the left side: (x + -20)(x + -20) = 640 Calculate the square root of the right side: 25.298221281 Break this problem into two subproblems by setting (x + -20) equal to 25.298221281 and -25.298221281.Subproblem 1
x + -20 = 25.298221281 Simplifying x + -20 = 25.298221281 Reorder the terms: -20 + x = 25.298221281 Solving -20 + x = 25.298221281 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 = 25.298221281 + 20 Combine like terms: -20 + 20 = 0 0 + x = 25.298221281 + 20 x = 25.298221281 + 20 Combine like terms: 25.298221281 + 20 = 45.298221281 x = 45.298221281 Simplifying x = 45.298221281Subproblem 2
x + -20 = -25.298221281 Simplifying x + -20 = -25.298221281 Reorder the terms: -20 + x = -25.298221281 Solving -20 + x = -25.298221281 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 = -25.298221281 + 20 Combine like terms: -20 + 20 = 0 0 + x = -25.298221281 + 20 x = -25.298221281 + 20 Combine like terms: -25.298221281 + 20 = -5.298221281 x = -5.298221281 Simplifying x = -5.298221281Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.298221281, -5.298221281}
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