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Simplifying -1x2 + -33.7x + -282.1 = 0 Reorder the terms: -282.1 + -33.7x + -1x2 = 0 Solving -282.1 + -33.7x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 282.1 + 33.7x + x2 = 0 Move the constant term to the right: Add '-282.1' to each side of the equation. 282.1 + 33.7x + -282.1 + x2 = 0 + -282.1 Reorder the terms: 282.1 + -282.1 + 33.7x + x2 = 0 + -282.1 Combine like terms: 282.1 + -282.1 = 0.0 0.0 + 33.7x + x2 = 0 + -282.1 33.7x + x2 = 0 + -282.1 Combine like terms: 0 + -282.1 = -282.1 33.7x + x2 = -282.1 The x term is 33.7x. Take half its coefficient (16.85). Square it (283.9225) and add it to both sides. Add '283.9225' to each side of the equation. 33.7x + 283.9225 + x2 = -282.1 + 283.9225 Reorder the terms: 283.9225 + 33.7x + x2 = -282.1 + 283.9225 Combine like terms: -282.1 + 283.9225 = 1.8225 283.9225 + 33.7x + x2 = 1.8225 Factor a perfect square on the left side: (x + 16.85)(x + 16.85) = 1.8225 Calculate the square root of the right side: 1.35 Break this problem into two subproblems by setting (x + 16.85) equal to 1.35 and -1.35.Subproblem 1
x + 16.85 = 1.35 Simplifying x + 16.85 = 1.35 Reorder the terms: 16.85 + x = 1.35 Solving 16.85 + x = 1.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.85' to each side of the equation. 16.85 + -16.85 + x = 1.35 + -16.85 Combine like terms: 16.85 + -16.85 = 0.00 0.00 + x = 1.35 + -16.85 x = 1.35 + -16.85 Combine like terms: 1.35 + -16.85 = -15.5 x = -15.5 Simplifying x = -15.5Subproblem 2
x + 16.85 = -1.35 Simplifying x + 16.85 = -1.35 Reorder the terms: 16.85 + x = -1.35 Solving 16.85 + x = -1.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.85' to each side of the equation. 16.85 + -16.85 + x = -1.35 + -16.85 Combine like terms: 16.85 + -16.85 = 0.00 0.00 + x = -1.35 + -16.85 x = -1.35 + -16.85 Combine like terms: -1.35 + -16.85 = -18.2 x = -18.2 Simplifying x = -18.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {-15.5, -18.2}
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