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Simplifying 0 = 0.2x2 + -25.5x + -17.4875 Reorder the terms: 0 = -17.4875 + -25.5x + 0.2x2 Solving 0 = -17.4875 + -25.5x + 0.2x2 Solving for variable 'x'. Combine like terms: 0 + 17.4875 = 17.4875 17.4875 + 25.5x + -0.2x2 = -17.4875 + -25.5x + 0.2x2 + 17.4875 + 25.5x + -0.2x2 Reorder the terms: 17.4875 + 25.5x + -0.2x2 = -17.4875 + 17.4875 + -25.5x + 25.5x + 0.2x2 + -0.2x2 Combine like terms: -17.4875 + 17.4875 = 0.0000 17.4875 + 25.5x + -0.2x2 = 0.0000 + -25.5x + 25.5x + 0.2x2 + -0.2x2 17.4875 + 25.5x + -0.2x2 = -25.5x + 25.5x + 0.2x2 + -0.2x2 Combine like terms: -25.5x + 25.5x = 0.0 17.4875 + 25.5x + -0.2x2 = 0.0 + 0.2x2 + -0.2x2 17.4875 + 25.5x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 17.4875 + 25.5x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -87.4375 + -127.5x + x2 = 0 Move the constant term to the right: Add '87.4375' to each side of the equation. -87.4375 + -127.5x + 87.4375 + x2 = 0 + 87.4375 Reorder the terms: -87.4375 + 87.4375 + -127.5x + x2 = 0 + 87.4375 Combine like terms: -87.4375 + 87.4375 = 0.0000 0.0000 + -127.5x + x2 = 0 + 87.4375 -127.5x + x2 = 0 + 87.4375 Combine like terms: 0 + 87.4375 = 87.4375 -127.5x + x2 = 87.4375 The x term is -127.5x. Take half its coefficient (-63.75). Square it (4064.0625) and add it to both sides. Add '4064.0625' to each side of the equation. -127.5x + 4064.0625 + x2 = 87.4375 + 4064.0625 Reorder the terms: 4064.0625 + -127.5x + x2 = 87.4375 + 4064.0625 Combine like terms: 87.4375 + 4064.0625 = 4151.5 4064.0625 + -127.5x + x2 = 4151.5 Factor a perfect square on the left side: (x + -63.75)(x + -63.75) = 4151.5 Calculate the square root of the right side: 64.43213484 Break this problem into two subproblems by setting (x + -63.75) equal to 64.43213484 and -64.43213484.Subproblem 1
x + -63.75 = 64.43213484 Simplifying x + -63.75 = 64.43213484 Reorder the terms: -63.75 + x = 64.43213484 Solving -63.75 + x = 64.43213484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '63.75' to each side of the equation. -63.75 + 63.75 + x = 64.43213484 + 63.75 Combine like terms: -63.75 + 63.75 = 0.00 0.00 + x = 64.43213484 + 63.75 x = 64.43213484 + 63.75 Combine like terms: 64.43213484 + 63.75 = 128.18213484 x = 128.18213484 Simplifying x = 128.18213484Subproblem 2
x + -63.75 = -64.43213484 Simplifying x + -63.75 = -64.43213484 Reorder the terms: -63.75 + x = -64.43213484 Solving -63.75 + x = -64.43213484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '63.75' to each side of the equation. -63.75 + 63.75 + x = -64.43213484 + 63.75 Combine like terms: -63.75 + 63.75 = 0.00 0.00 + x = -64.43213484 + 63.75 x = -64.43213484 + 63.75 Combine like terms: -64.43213484 + 63.75 = -0.68213484 x = -0.68213484 Simplifying x = -0.68213484Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.18213484, -0.68213484}
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