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Simplifying -1.738x2 + 38.528x + 384.032 = 560 Reorder the terms: 384.032 + 38.528x + -1.738x2 = 560 Solving 384.032 + 38.528x + -1.738x2 = 560 Solving for variable 'x'. Reorder the terms: 384.032 + -560 + 38.528x + -1.738x2 = 560 + -560 Combine like terms: 384.032 + -560 = -175.968 -175.968 + 38.528x + -1.738x2 = 560 + -560 Combine like terms: 560 + -560 = 0 -175.968 + 38.528x + -1.738x2 = 0 Begin completing the square. Divide all terms by -1.738 the coefficient of the squared term: Divide each side by '-1.738'. 101.2474108 + -22.16800921x + x2 = 0 Move the constant term to the right: Add '-101.2474108' to each side of the equation. 101.2474108 + -22.16800921x + -101.2474108 + x2 = 0 + -101.2474108 Reorder the terms: 101.2474108 + -101.2474108 + -22.16800921x + x2 = 0 + -101.2474108 Combine like terms: 101.2474108 + -101.2474108 = 0.0000000 0.0000000 + -22.16800921x + x2 = 0 + -101.2474108 -22.16800921x + x2 = 0 + -101.2474108 Combine like terms: 0 + -101.2474108 = -101.2474108 -22.16800921x + x2 = -101.2474108 The x term is -22.16800921x. Take half its coefficient (-11.08400461). Square it (122.8551582) and add it to both sides. Add '122.8551582' to each side of the equation. -22.16800921x + 122.8551582 + x2 = -101.2474108 + 122.8551582 Reorder the terms: 122.8551582 + -22.16800921x + x2 = -101.2474108 + 122.8551582 Combine like terms: -101.2474108 + 122.8551582 = 21.6077474 122.8551582 + -22.16800921x + x2 = 21.6077474 Factor a perfect square on the left side: (x + -11.08400461)(x + -11.08400461) = 21.6077474 Calculate the square root of the right side: 4.648413428 Break this problem into two subproblems by setting (x + -11.08400461) equal to 4.648413428 and -4.648413428.Subproblem 1
x + -11.08400461 = 4.648413428 Simplifying x + -11.08400461 = 4.648413428 Reorder the terms: -11.08400461 + x = 4.648413428 Solving -11.08400461 + x = 4.648413428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.08400461' to each side of the equation. -11.08400461 + 11.08400461 + x = 4.648413428 + 11.08400461 Combine like terms: -11.08400461 + 11.08400461 = 0.00000000 0.00000000 + x = 4.648413428 + 11.08400461 x = 4.648413428 + 11.08400461 Combine like terms: 4.648413428 + 11.08400461 = 15.732418038 x = 15.732418038 Simplifying x = 15.732418038Subproblem 2
x + -11.08400461 = -4.648413428 Simplifying x + -11.08400461 = -4.648413428 Reorder the terms: -11.08400461 + x = -4.648413428 Solving -11.08400461 + x = -4.648413428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.08400461' to each side of the equation. -11.08400461 + 11.08400461 + x = -4.648413428 + 11.08400461 Combine like terms: -11.08400461 + 11.08400461 = 0.00000000 0.00000000 + x = -4.648413428 + 11.08400461 x = -4.648413428 + 11.08400461 Combine like terms: -4.648413428 + 11.08400461 = 6.435591182 x = 6.435591182 Simplifying x = 6.435591182Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.732418038, 6.435591182}
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