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Simplifying 0 = -2x2 + 101x + -570 Reorder the terms: 0 = -570 + 101x + -2x2 Solving 0 = -570 + 101x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 570 = 570 570 + -101x + 2x2 = -570 + 101x + -2x2 + 570 + -101x + 2x2 Reorder the terms: 570 + -101x + 2x2 = -570 + 570 + 101x + -101x + -2x2 + 2x2 Combine like terms: -570 + 570 = 0 570 + -101x + 2x2 = 0 + 101x + -101x + -2x2 + 2x2 570 + -101x + 2x2 = 101x + -101x + -2x2 + 2x2 Combine like terms: 101x + -101x = 0 570 + -101x + 2x2 = 0 + -2x2 + 2x2 570 + -101x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 570 + -101x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 285 + -50.5x + x2 = 0 Move the constant term to the right: Add '-285' to each side of the equation. 285 + -50.5x + -285 + x2 = 0 + -285 Reorder the terms: 285 + -285 + -50.5x + x2 = 0 + -285 Combine like terms: 285 + -285 = 0 0 + -50.5x + x2 = 0 + -285 -50.5x + x2 = 0 + -285 Combine like terms: 0 + -285 = -285 -50.5x + x2 = -285 The x term is -50.5x. Take half its coefficient (-25.25). Square it (637.5625) and add it to both sides. Add '637.5625' to each side of the equation. -50.5x + 637.5625 + x2 = -285 + 637.5625 Reorder the terms: 637.5625 + -50.5x + x2 = -285 + 637.5625 Combine like terms: -285 + 637.5625 = 352.5625 637.5625 + -50.5x + x2 = 352.5625 Factor a perfect square on the left side: (x + -25.25)(x + -25.25) = 352.5625 Calculate the square root of the right side: 18.776647731 Break this problem into two subproblems by setting (x + -25.25) equal to 18.776647731 and -18.776647731.Subproblem 1
x + -25.25 = 18.776647731 Simplifying x + -25.25 = 18.776647731 Reorder the terms: -25.25 + x = 18.776647731 Solving -25.25 + x = 18.776647731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.25' to each side of the equation. -25.25 + 25.25 + x = 18.776647731 + 25.25 Combine like terms: -25.25 + 25.25 = 0.00 0.00 + x = 18.776647731 + 25.25 x = 18.776647731 + 25.25 Combine like terms: 18.776647731 + 25.25 = 44.026647731 x = 44.026647731 Simplifying x = 44.026647731Subproblem 2
x + -25.25 = -18.776647731 Simplifying x + -25.25 = -18.776647731 Reorder the terms: -25.25 + x = -18.776647731 Solving -25.25 + x = -18.776647731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.25' to each side of the equation. -25.25 + 25.25 + x = -18.776647731 + 25.25 Combine like terms: -25.25 + 25.25 = 0.00 0.00 + x = -18.776647731 + 25.25 x = -18.776647731 + 25.25 Combine like terms: -18.776647731 + 25.25 = 6.473352269 x = 6.473352269 Simplifying x = 6.473352269Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.026647731, 6.473352269}
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