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Simplifying 5x2 + -92x + 360 = 0 Reorder the terms: 360 + -92x + 5x2 = 0 Solving 360 + -92x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 72 + -18.4x + x2 = 0 Move the constant term to the right: Add '-72' to each side of the equation. 72 + -18.4x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -18.4x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -18.4x + x2 = 0 + -72 -18.4x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -18.4x + x2 = -72 The x term is -18.4x. Take half its coefficient (-9.2). Square it (84.64) and add it to both sides. Add '84.64' to each side of the equation. -18.4x + 84.64 + x2 = -72 + 84.64 Reorder the terms: 84.64 + -18.4x + x2 = -72 + 84.64 Combine like terms: -72 + 84.64 = 12.64 84.64 + -18.4x + x2 = 12.64 Factor a perfect square on the left side: (x + -9.2)(x + -9.2) = 12.64 Calculate the square root of the right side: 3.555277767 Break this problem into two subproblems by setting (x + -9.2) equal to 3.555277767 and -3.555277767.Subproblem 1
x + -9.2 = 3.555277767 Simplifying x + -9.2 = 3.555277767 Reorder the terms: -9.2 + x = 3.555277767 Solving -9.2 + x = 3.555277767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.2' to each side of the equation. -9.2 + 9.2 + x = 3.555277767 + 9.2 Combine like terms: -9.2 + 9.2 = 0.0 0.0 + x = 3.555277767 + 9.2 x = 3.555277767 + 9.2 Combine like terms: 3.555277767 + 9.2 = 12.755277767 x = 12.755277767 Simplifying x = 12.755277767Subproblem 2
x + -9.2 = -3.555277767 Simplifying x + -9.2 = -3.555277767 Reorder the terms: -9.2 + x = -3.555277767 Solving -9.2 + x = -3.555277767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.2' to each side of the equation. -9.2 + 9.2 + x = -3.555277767 + 9.2 Combine like terms: -9.2 + 9.2 = 0.0 0.0 + x = -3.555277767 + 9.2 x = -3.555277767 + 9.2 Combine like terms: -3.555277767 + 9.2 = 5.644722233 x = 5.644722233 Simplifying x = 5.644722233Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.755277767, 5.644722233}
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