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Simplifying 519.84 = x(x + 22.8) Reorder the terms: 519.84 = x(22.8 + x) 519.84 = (22.8 * x + x * x) 519.84 = (22.8x + x2) Solving 519.84 = 22.8x + x2 Solving for variable 'x'. Reorder the terms: 519.84 + -22.8x + -1x2 = 22.8x + -22.8x + x2 + -1x2 Combine like terms: 22.8x + -22.8x = 0.0 519.84 + -22.8x + -1x2 = 0.0 + x2 + -1x2 519.84 + -22.8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 519.84 + -22.8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -519.84 + 22.8x + x2 = 0 Move the constant term to the right: Add '519.84' to each side of the equation. -519.84 + 22.8x + 519.84 + x2 = 0 + 519.84 Reorder the terms: -519.84 + 519.84 + 22.8x + x2 = 0 + 519.84 Combine like terms: -519.84 + 519.84 = 0.00 0.00 + 22.8x + x2 = 0 + 519.84 22.8x + x2 = 0 + 519.84 Combine like terms: 0 + 519.84 = 519.84 22.8x + x2 = 519.84 The x term is 22.8x. Take half its coefficient (11.4). Square it (129.96) and add it to both sides. Add '129.96' to each side of the equation. 22.8x + 129.96 + x2 = 519.84 + 129.96 Reorder the terms: 129.96 + 22.8x + x2 = 519.84 + 129.96 Combine like terms: 519.84 + 129.96 = 649.8 129.96 + 22.8x + x2 = 649.8 Factor a perfect square on the left side: (x + 11.4)(x + 11.4) = 649.8 Calculate the square root of the right side: 25.491174943 Break this problem into two subproblems by setting (x + 11.4) equal to 25.491174943 and -25.491174943.Subproblem 1
x + 11.4 = 25.491174943 Simplifying x + 11.4 = 25.491174943 Reorder the terms: 11.4 + x = 25.491174943 Solving 11.4 + x = 25.491174943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.4' to each side of the equation. 11.4 + -11.4 + x = 25.491174943 + -11.4 Combine like terms: 11.4 + -11.4 = 0.0 0.0 + x = 25.491174943 + -11.4 x = 25.491174943 + -11.4 Combine like terms: 25.491174943 + -11.4 = 14.091174943 x = 14.091174943 Simplifying x = 14.091174943Subproblem 2
x + 11.4 = -25.491174943 Simplifying x + 11.4 = -25.491174943 Reorder the terms: 11.4 + x = -25.491174943 Solving 11.4 + x = -25.491174943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.4' to each side of the equation. 11.4 + -11.4 + x = -25.491174943 + -11.4 Combine like terms: 11.4 + -11.4 = 0.0 0.0 + x = -25.491174943 + -11.4 x = -25.491174943 + -11.4 Combine like terms: -25.491174943 + -11.4 = -36.891174943 x = -36.891174943 Simplifying x = -36.891174943Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.091174943, -36.891174943}
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