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Simplifying 324.2 + -58.5x + 1.25x2 = 0 Solving 324.2 + -58.5x + 1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. 259.36 + -46.8x + x2 = 0 Move the constant term to the right: Add '-259.36' to each side of the equation. 259.36 + -46.8x + -259.36 + x2 = 0 + -259.36 Reorder the terms: 259.36 + -259.36 + -46.8x + x2 = 0 + -259.36 Combine like terms: 259.36 + -259.36 = 0.00 0.00 + -46.8x + x2 = 0 + -259.36 -46.8x + x2 = 0 + -259.36 Combine like terms: 0 + -259.36 = -259.36 -46.8x + x2 = -259.36 The x term is -46.8x. Take half its coefficient (-23.4). Square it (547.56) and add it to both sides. Add '547.56' to each side of the equation. -46.8x + 547.56 + x2 = -259.36 + 547.56 Reorder the terms: 547.56 + -46.8x + x2 = -259.36 + 547.56 Combine like terms: -259.36 + 547.56 = 288.2 547.56 + -46.8x + x2 = 288.2 Factor a perfect square on the left side: (x + -23.4)(x + -23.4) = 288.2 Calculate the square root of the right side: 16.976454282 Break this problem into two subproblems by setting (x + -23.4) equal to 16.976454282 and -16.976454282.Subproblem 1
x + -23.4 = 16.976454282 Simplifying x + -23.4 = 16.976454282 Reorder the terms: -23.4 + x = 16.976454282 Solving -23.4 + x = 16.976454282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.4' to each side of the equation. -23.4 + 23.4 + x = 16.976454282 + 23.4 Combine like terms: -23.4 + 23.4 = 0.0 0.0 + x = 16.976454282 + 23.4 x = 16.976454282 + 23.4 Combine like terms: 16.976454282 + 23.4 = 40.376454282 x = 40.376454282 Simplifying x = 40.376454282Subproblem 2
x + -23.4 = -16.976454282 Simplifying x + -23.4 = -16.976454282 Reorder the terms: -23.4 + x = -16.976454282 Solving -23.4 + x = -16.976454282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.4' to each side of the equation. -23.4 + 23.4 + x = -16.976454282 + 23.4 Combine like terms: -23.4 + 23.4 = 0.0 0.0 + x = -16.976454282 + 23.4 x = -16.976454282 + 23.4 Combine like terms: -16.976454282 + 23.4 = 6.423545718 x = 6.423545718 Simplifying x = 6.423545718Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.376454282, 6.423545718}
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