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Simplifying 1048x2 + -80x + -1080 = 0 Reorder the terms: -1080 + -80x + 1048x2 = 0 Solving -1080 + -80x + 1048x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-135 + -10x + 131x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-135 + -10x + 131x2)' equal to zero and attempt to solve: Simplifying -135 + -10x + 131x2 = 0 Solving -135 + -10x + 131x2 = 0 Begin completing the square. Divide all terms by 131 the coefficient of the squared term: Divide each side by '131'. -1.030534351 + -0.07633587786x + x2 = 0 Move the constant term to the right: Add '1.030534351' to each side of the equation. -1.030534351 + -0.07633587786x + 1.030534351 + x2 = 0 + 1.030534351 Reorder the terms: -1.030534351 + 1.030534351 + -0.07633587786x + x2 = 0 + 1.030534351 Combine like terms: -1.030534351 + 1.030534351 = 0.000000000 0.000000000 + -0.07633587786x + x2 = 0 + 1.030534351 -0.07633587786x + x2 = 0 + 1.030534351 Combine like terms: 0 + 1.030534351 = 1.030534351 -0.07633587786x + x2 = 1.030534351 The x term is -0.07633587786x. Take half its coefficient (-0.03816793893). Square it (0.001456791562) and add it to both sides. Add '0.001456791562' to each side of the equation. -0.07633587786x + 0.001456791562 + x2 = 1.030534351 + 0.001456791562 Reorder the terms: 0.001456791562 + -0.07633587786x + x2 = 1.030534351 + 0.001456791562 Combine like terms: 1.030534351 + 0.001456791562 = 1.031991142562 0.001456791562 + -0.07633587786x + x2 = 1.031991142562 Factor a perfect square on the left side: (x + -0.03816793893)(x + -0.03816793893) = 1.031991142562 Calculate the square root of the right side: 1.015869648 Break this problem into two subproblems by setting (x + -0.03816793893) equal to 1.015869648 and -1.015869648.Subproblem 1
x + -0.03816793893 = 1.015869648 Simplifying x + -0.03816793893 = 1.015869648 Reorder the terms: -0.03816793893 + x = 1.015869648 Solving -0.03816793893 + x = 1.015869648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03816793893' to each side of the equation. -0.03816793893 + 0.03816793893 + x = 1.015869648 + 0.03816793893 Combine like terms: -0.03816793893 + 0.03816793893 = 0.00000000000 0.00000000000 + x = 1.015869648 + 0.03816793893 x = 1.015869648 + 0.03816793893 Combine like terms: 1.015869648 + 0.03816793893 = 1.05403758693 x = 1.05403758693 Simplifying x = 1.05403758693Subproblem 2
x + -0.03816793893 = -1.015869648 Simplifying x + -0.03816793893 = -1.015869648 Reorder the terms: -0.03816793893 + x = -1.015869648 Solving -0.03816793893 + x = -1.015869648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03816793893' to each side of the equation. -0.03816793893 + 0.03816793893 + x = -1.015869648 + 0.03816793893 Combine like terms: -0.03816793893 + 0.03816793893 = 0.00000000000 0.00000000000 + x = -1.015869648 + 0.03816793893 x = -1.015869648 + 0.03816793893 Combine like terms: -1.015869648 + 0.03816793893 = -0.97770170907 x = -0.97770170907 Simplifying x = -0.97770170907Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.05403758693, -0.97770170907}Solution
x = {1.05403758693, -0.97770170907}
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