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Simplifying x = 1200 + 70x + -5x2 Solving x = 1200 + 70x + -5x2 Solving for variable 'x'. Reorder the terms: -1200 + x + -70x + 5x2 = 1200 + 70x + -5x2 + -1200 + -70x + 5x2 Combine like terms: x + -70x = -69x -1200 + -69x + 5x2 = 1200 + 70x + -5x2 + -1200 + -70x + 5x2 Reorder the terms: -1200 + -69x + 5x2 = 1200 + -1200 + 70x + -70x + -5x2 + 5x2 Combine like terms: 1200 + -1200 = 0 -1200 + -69x + 5x2 = 0 + 70x + -70x + -5x2 + 5x2 -1200 + -69x + 5x2 = 70x + -70x + -5x2 + 5x2 Combine like terms: 70x + -70x = 0 -1200 + -69x + 5x2 = 0 + -5x2 + 5x2 -1200 + -69x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -1200 + -69x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -240 + -13.8x + x2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + -13.8x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -13.8x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -13.8x + x2 = 0 + 240 -13.8x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -13.8x + x2 = 240 The x term is -13.8x. Take half its coefficient (-6.9). Square it (47.61) and add it to both sides. Add '47.61' to each side of the equation. -13.8x + 47.61 + x2 = 240 + 47.61 Reorder the terms: 47.61 + -13.8x + x2 = 240 + 47.61 Combine like terms: 240 + 47.61 = 287.61 47.61 + -13.8x + x2 = 287.61 Factor a perfect square on the left side: (x + -6.9)(x + -6.9) = 287.61 Calculate the square root of the right side: 16.959068371 Break this problem into two subproblems by setting (x + -6.9) equal to 16.959068371 and -16.959068371.Subproblem 1
x + -6.9 = 16.959068371 Simplifying x + -6.9 = 16.959068371 Reorder the terms: -6.9 + x = 16.959068371 Solving -6.9 + x = 16.959068371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.9' to each side of the equation. -6.9 + 6.9 + x = 16.959068371 + 6.9 Combine like terms: -6.9 + 6.9 = 0.0 0.0 + x = 16.959068371 + 6.9 x = 16.959068371 + 6.9 Combine like terms: 16.959068371 + 6.9 = 23.859068371 x = 23.859068371 Simplifying x = 23.859068371Subproblem 2
x + -6.9 = -16.959068371 Simplifying x + -6.9 = -16.959068371 Reorder the terms: -6.9 + x = -16.959068371 Solving -6.9 + x = -16.959068371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.9' to each side of the equation. -6.9 + 6.9 + x = -16.959068371 + 6.9 Combine like terms: -6.9 + 6.9 = 0.0 0.0 + x = -16.959068371 + 6.9 x = -16.959068371 + 6.9 Combine like terms: -16.959068371 + 6.9 = -10.059068371 x = -10.059068371 Simplifying x = -10.059068371Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.859068371, -10.059068371}
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