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Simplifying 9.9x = -4.9x2 + 24.5x + 9.9 Reorder the terms: 9.9x = 9.9 + 24.5x + -4.9x2 Solving 9.9x = 9.9 + 24.5x + -4.9x2 Solving for variable 'x'. Reorder the terms: -9.9 + 9.9x + -24.5x + 4.9x2 = 9.9 + 24.5x + -4.9x2 + -9.9 + -24.5x + 4.9x2 Combine like terms: 9.9x + -24.5x = -14.6x -9.9 + -14.6x + 4.9x2 = 9.9 + 24.5x + -4.9x2 + -9.9 + -24.5x + 4.9x2 Reorder the terms: -9.9 + -14.6x + 4.9x2 = 9.9 + -9.9 + 24.5x + -24.5x + -4.9x2 + 4.9x2 Combine like terms: 9.9 + -9.9 = 0.0 -9.9 + -14.6x + 4.9x2 = 0.0 + 24.5x + -24.5x + -4.9x2 + 4.9x2 -9.9 + -14.6x + 4.9x2 = 24.5x + -24.5x + -4.9x2 + 4.9x2 Combine like terms: 24.5x + -24.5x = 0.0 -9.9 + -14.6x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -9.9 + -14.6x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -9.9 + -14.6x + 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'. -2.020408163 + -2.979591837x + x2 = 0 Move the constant term to the right: Add '2.020408163' to each side of the equation. -2.020408163 + -2.979591837x + 2.020408163 + x2 = 0 + 2.020408163 Reorder the terms: -2.020408163 + 2.020408163 + -2.979591837x + x2 = 0 + 2.020408163 Combine like terms: -2.020408163 + 2.020408163 = 0.000000000 0.000000000 + -2.979591837x + x2 = 0 + 2.020408163 -2.979591837x + x2 = 0 + 2.020408163 Combine like terms: 0 + 2.020408163 = 2.020408163 -2.979591837x + x2 = 2.020408163 The x term is -2.979591837x. Take half its coefficient (-1.489795919). Square it (2.219491880) and add it to both sides. Add '2.219491880' to each side of the equation. -2.979591837x + 2.219491880 + x2 = 2.020408163 + 2.219491880 Reorder the terms: 2.219491880 + -2.979591837x + x2 = 2.020408163 + 2.219491880 Combine like terms: 2.020408163 + 2.219491880 = 4.239900043 2.219491880 + -2.979591837x + x2 = 4.239900043 Factor a perfect square on the left side: (x + -1.489795919)(x + -1.489795919) = 4.239900043 Calculate the square root of the right side: 2.059101756 Break this problem into two subproblems by setting (x + -1.489795919) equal to 2.059101756 and -2.059101756.Subproblem 1
x + -1.489795919 = 2.059101756 Simplifying x + -1.489795919 = 2.059101756 Reorder the terms: -1.489795919 + x = 2.059101756 Solving -1.489795919 + x = 2.059101756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.489795919' to each side of the equation. -1.489795919 + 1.489795919 + x = 2.059101756 + 1.489795919 Combine like terms: -1.489795919 + 1.489795919 = 0.000000000 0.000000000 + x = 2.059101756 + 1.489795919 x = 2.059101756 + 1.489795919 Combine like terms: 2.059101756 + 1.489795919 = 3.548897675 x = 3.548897675 Simplifying x = 3.548897675Subproblem 2
x + -1.489795919 = -2.059101756 Simplifying x + -1.489795919 = -2.059101756 Reorder the terms: -1.489795919 + x = -2.059101756 Solving -1.489795919 + x = -2.059101756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.489795919' to each side of the equation. -1.489795919 + 1.489795919 + x = -2.059101756 + 1.489795919 Combine like terms: -1.489795919 + 1.489795919 = 0.000000000 0.000000000 + x = -2.059101756 + 1.489795919 x = -2.059101756 + 1.489795919 Combine like terms: -2.059101756 + 1.489795919 = -0.569305837 x = -0.569305837 Simplifying x = -0.569305837Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.548897675, -0.569305837}
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