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Simplifying 16 = -71.88x + -4.9x2 Solving 16 = -71.88x + -4.9x2 Solving for variable 'x'. Reorder the terms: 16 + 71.88x + 4.9x2 = -71.88x + 71.88x + -4.9x2 + 4.9x2 Combine like terms: -71.88x + 71.88x = 0.00 16 + 71.88x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 16 + 71.88x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 16 + 71.88x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 3.265306122 + 14.66938776x + x2 = 0 Move the constant term to the right: Add '-3.265306122' to each side of the equation. 3.265306122 + 14.66938776x + -3.265306122 + x2 = 0 + -3.265306122 Reorder the terms: 3.265306122 + -3.265306122 + 14.66938776x + x2 = 0 + -3.265306122 Combine like terms: 3.265306122 + -3.265306122 = 0.000000000 0.000000000 + 14.66938776x + x2 = 0 + -3.265306122 14.66938776x + x2 = 0 + -3.265306122 Combine like terms: 0 + -3.265306122 = -3.265306122 14.66938776x + x2 = -3.265306122 The x term is 14.66938776x. Take half its coefficient (7.33469388). Square it (53.79773431) and add it to both sides. Add '53.79773431' to each side of the equation. 14.66938776x + 53.79773431 + x2 = -3.265306122 + 53.79773431 Reorder the terms: 53.79773431 + 14.66938776x + x2 = -3.265306122 + 53.79773431 Combine like terms: -3.265306122 + 53.79773431 = 50.532428188 53.79773431 + 14.66938776x + x2 = 50.532428188 Factor a perfect square on the left side: (x + 7.33469388)(x + 7.33469388) = 50.532428188 Calculate the square root of the right side: 7.108616475 Break this problem into two subproblems by setting (x + 7.33469388) equal to 7.108616475 and -7.108616475.Subproblem 1
x + 7.33469388 = 7.108616475 Simplifying x + 7.33469388 = 7.108616475 Reorder the terms: 7.33469388 + x = 7.108616475 Solving 7.33469388 + x = 7.108616475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.33469388' to each side of the equation. 7.33469388 + -7.33469388 + x = 7.108616475 + -7.33469388 Combine like terms: 7.33469388 + -7.33469388 = 0.00000000 0.00000000 + x = 7.108616475 + -7.33469388 x = 7.108616475 + -7.33469388 Combine like terms: 7.108616475 + -7.33469388 = -0.226077405 x = -0.226077405 Simplifying x = -0.226077405Subproblem 2
x + 7.33469388 = -7.108616475 Simplifying x + 7.33469388 = -7.108616475 Reorder the terms: 7.33469388 + x = -7.108616475 Solving 7.33469388 + x = -7.108616475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.33469388' to each side of the equation. 7.33469388 + -7.33469388 + x = -7.108616475 + -7.33469388 Combine like terms: 7.33469388 + -7.33469388 = 0.00000000 0.00000000 + x = -7.108616475 + -7.33469388 x = -7.108616475 + -7.33469388 Combine like terms: -7.108616475 + -7.33469388 = -14.443310355 x = -14.443310355 Simplifying x = -14.443310355Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.226077405, -14.443310355}
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