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Simplifying 49 = -0.095x2 + 1.74x + 60 Reorder the terms: 49 = 60 + 1.74x + -0.095x2 Solving 49 = 60 + 1.74x + -0.095x2 Solving for variable 'x'. Combine like terms: 49 + -60 = -11 -11 + -1.74x + 0.095x2 = 60 + 1.74x + -0.095x2 + -60 + -1.74x + 0.095x2 Reorder the terms: -11 + -1.74x + 0.095x2 = 60 + -60 + 1.74x + -1.74x + -0.095x2 + 0.095x2 Combine like terms: 60 + -60 = 0 -11 + -1.74x + 0.095x2 = 0 + 1.74x + -1.74x + -0.095x2 + 0.095x2 -11 + -1.74x + 0.095x2 = 1.74x + -1.74x + -0.095x2 + 0.095x2 Combine like terms: 1.74x + -1.74x = 0.00 -11 + -1.74x + 0.095x2 = 0.00 + -0.095x2 + 0.095x2 -11 + -1.74x + 0.095x2 = -0.095x2 + 0.095x2 Combine like terms: -0.095x2 + 0.095x2 = 0.000 -11 + -1.74x + 0.095x2 = 0.000 Begin completing the square. Divide all terms by 0.095 the coefficient of the squared term: Divide each side by '0.095'. -115.7894737 + -18.31578947x + x2 = 0 Move the constant term to the right: Add '115.7894737' to each side of the equation. -115.7894737 + -18.31578947x + 115.7894737 + x2 = 0 + 115.7894737 Reorder the terms: -115.7894737 + 115.7894737 + -18.31578947x + x2 = 0 + 115.7894737 Combine like terms: -115.7894737 + 115.7894737 = 0.0000000 0.0000000 + -18.31578947x + x2 = 0 + 115.7894737 -18.31578947x + x2 = 0 + 115.7894737 Combine like terms: 0 + 115.7894737 = 115.7894737 -18.31578947x + x2 = 115.7894737 The x term is -18.31578947x. Take half its coefficient (-9.157894735). Square it (83.86703598) and add it to both sides. Add '83.86703598' to each side of the equation. -18.31578947x + 83.86703598 + x2 = 115.7894737 + 83.86703598 Reorder the terms: 83.86703598 + -18.31578947x + x2 = 115.7894737 + 83.86703598 Combine like terms: 115.7894737 + 83.86703598 = 199.65650968 83.86703598 + -18.31578947x + x2 = 199.65650968 Factor a perfect square on the left side: (x + -9.157894735)(x + -9.157894735) = 199.65650968 Calculate the square root of the right side: 14.129986188 Break this problem into two subproblems by setting (x + -9.157894735) equal to 14.129986188 and -14.129986188.Subproblem 1
x + -9.157894735 = 14.129986188 Simplifying x + -9.157894735 = 14.129986188 Reorder the terms: -9.157894735 + x = 14.129986188 Solving -9.157894735 + x = 14.129986188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.157894735' to each side of the equation. -9.157894735 + 9.157894735 + x = 14.129986188 + 9.157894735 Combine like terms: -9.157894735 + 9.157894735 = 0.000000000 0.000000000 + x = 14.129986188 + 9.157894735 x = 14.129986188 + 9.157894735 Combine like terms: 14.129986188 + 9.157894735 = 23.287880923 x = 23.287880923 Simplifying x = 23.287880923Subproblem 2
x + -9.157894735 = -14.129986188 Simplifying x + -9.157894735 = -14.129986188 Reorder the terms: -9.157894735 + x = -14.129986188 Solving -9.157894735 + x = -14.129986188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.157894735' to each side of the equation. -9.157894735 + 9.157894735 + x = -14.129986188 + 9.157894735 Combine like terms: -9.157894735 + 9.157894735 = 0.000000000 0.000000000 + x = -14.129986188 + 9.157894735 x = -14.129986188 + 9.157894735 Combine like terms: -14.129986188 + 9.157894735 = -4.972091453 x = -4.972091453 Simplifying x = -4.972091453Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.287880923, -4.972091453}
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