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Simplifying -14.84x2 + 189.95x + 2445.88 = 0 Reorder the terms: 2445.88 + 189.95x + -14.84x2 = 0 Solving 2445.88 + 189.95x + -14.84x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -14.84 the coefficient of the squared term: Divide each side by '-14.84'. -164.8167116 + -12.79986523x + x2 = 0 Move the constant term to the right: Add '164.8167116' to each side of the equation. -164.8167116 + -12.79986523x + 164.8167116 + x2 = 0 + 164.8167116 Reorder the terms: -164.8167116 + 164.8167116 + -12.79986523x + x2 = 0 + 164.8167116 Combine like terms: -164.8167116 + 164.8167116 = 0.0000000 0.0000000 + -12.79986523x + x2 = 0 + 164.8167116 -12.79986523x + x2 = 0 + 164.8167116 Combine like terms: 0 + 164.8167116 = 164.8167116 -12.79986523x + x2 = 164.8167116 The x term is -12.79986523x. Take half its coefficient (-6.399932615). Square it (40.95913748) and add it to both sides. Add '40.95913748' to each side of the equation. -12.79986523x + 40.95913748 + x2 = 164.8167116 + 40.95913748 Reorder the terms: 40.95913748 + -12.79986523x + x2 = 164.8167116 + 40.95913748 Combine like terms: 164.8167116 + 40.95913748 = 205.77584908 40.95913748 + -12.79986523x + x2 = 205.77584908 Factor a perfect square on the left side: (x + -6.399932615)(x + -6.399932615) = 205.77584908 Calculate the square root of the right side: 14.344889302 Break this problem into two subproblems by setting (x + -6.399932615) equal to 14.344889302 and -14.344889302.Subproblem 1
x + -6.399932615 = 14.344889302 Simplifying x + -6.399932615 = 14.344889302 Reorder the terms: -6.399932615 + x = 14.344889302 Solving -6.399932615 + x = 14.344889302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.399932615' to each side of the equation. -6.399932615 + 6.399932615 + x = 14.344889302 + 6.399932615 Combine like terms: -6.399932615 + 6.399932615 = 0.000000000 0.000000000 + x = 14.344889302 + 6.399932615 x = 14.344889302 + 6.399932615 Combine like terms: 14.344889302 + 6.399932615 = 20.744821917 x = 20.744821917 Simplifying x = 20.744821917Subproblem 2
x + -6.399932615 = -14.344889302 Simplifying x + -6.399932615 = -14.344889302 Reorder the terms: -6.399932615 + x = -14.344889302 Solving -6.399932615 + x = -14.344889302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.399932615' to each side of the equation. -6.399932615 + 6.399932615 + x = -14.344889302 + 6.399932615 Combine like terms: -6.399932615 + 6.399932615 = 0.000000000 0.000000000 + x = -14.344889302 + 6.399932615 x = -14.344889302 + 6.399932615 Combine like terms: -14.344889302 + 6.399932615 = -7.944956687 x = -7.944956687 Simplifying x = -7.944956687Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.744821917, -7.944956687}
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