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Simplifying 43469.88 = x(265.1 + 315.2 + 197.5 + x) Combine like terms: 265.1 + 315.2 = 580.3 43469.88 = x(580.3 + 197.5 + x) Combine like terms: 580.3 + 197.5 = 777.8 43469.88 = x(777.8 + x) 43469.88 = (777.8 * x + x * x) 43469.88 = (777.8x + x2) Solving 43469.88 = 777.8x + x2 Solving for variable 'x'. Reorder the terms: 43469.88 + -777.8x + -1x2 = 777.8x + -777.8x + x2 + -1x2 Combine like terms: 777.8x + -777.8x = 0.0 43469.88 + -777.8x + -1x2 = 0.0 + x2 + -1x2 43469.88 + -777.8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 43469.88 + -777.8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -43469.88 + 777.8x + x2 = 0 Move the constant term to the right: Add '43469.88' to each side of the equation. -43469.88 + 777.8x + 43469.88 + x2 = 0 + 43469.88 Reorder the terms: -43469.88 + 43469.88 + 777.8x + x2 = 0 + 43469.88 Combine like terms: -43469.88 + 43469.88 = 0.00 0.00 + 777.8x + x2 = 0 + 43469.88 777.8x + x2 = 0 + 43469.88 Combine like terms: 0 + 43469.88 = 43469.88 777.8x + x2 = 43469.88 The x term is 777.8x. Take half its coefficient (388.9). Square it (151243.21) and add it to both sides. Add '151243.21' to each side of the equation. 777.8x + 151243.21 + x2 = 43469.88 + 151243.21 Reorder the terms: 151243.21 + 777.8x + x2 = 43469.88 + 151243.21 Combine like terms: 43469.88 + 151243.21 = 194713.09 151243.21 + 777.8x + x2 = 194713.09 Factor a perfect square on the left side: (x + 388.9)(x + 388.9) = 194713.09 Calculate the square root of the right side: 441.26306213 Break this problem into two subproblems by setting (x + 388.9) equal to 441.26306213 and -441.26306213.Subproblem 1
x + 388.9 = 441.26306213 Simplifying x + 388.9 = 441.26306213 Reorder the terms: 388.9 + x = 441.26306213 Solving 388.9 + x = 441.26306213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-388.9' to each side of the equation. 388.9 + -388.9 + x = 441.26306213 + -388.9 Combine like terms: 388.9 + -388.9 = 0.0 0.0 + x = 441.26306213 + -388.9 x = 441.26306213 + -388.9 Combine like terms: 441.26306213 + -388.9 = 52.36306213 x = 52.36306213 Simplifying x = 52.36306213Subproblem 2
x + 388.9 = -441.26306213 Simplifying x + 388.9 = -441.26306213 Reorder the terms: 388.9 + x = -441.26306213 Solving 388.9 + x = -441.26306213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-388.9' to each side of the equation. 388.9 + -388.9 + x = -441.26306213 + -388.9 Combine like terms: 388.9 + -388.9 = 0.0 0.0 + x = -441.26306213 + -388.9 x = -441.26306213 + -388.9 Combine like terms: -441.26306213 + -388.9 = -830.16306213 x = -830.16306213 Simplifying x = -830.16306213Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.36306213, -830.16306213}
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