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Simplifying 9.8x2 + -10x + -60 = 0 Reorder the terms: -60 + -10x + 9.8x2 = 0 Solving -60 + -10x + 9.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -6.12244898 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + -1.020408163x + 6.12244898 + x2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + -1.020408163x + x2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + -1.020408163x + x2 = 0 + 6.12244898 -1.020408163x + x2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 -1.020408163x + x2 = 6.12244898 The x term is -1.020408163x. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163x + 0.2603082048 + x2 = 6.12244898 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 6.12244898 + 0.2603082048 Combine like terms: 6.12244898 + 0.2603082048 = 6.3827571848 0.2603082048 + -1.020408163x + x2 = 6.3827571848 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 6.3827571848 Calculate the square root of the right side: 2.526411919 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 2.526411919 and -2.526411919.Subproblem 1
x + -0.5102040815 = 2.526411919 Simplifying x + -0.5102040815 = 2.526411919 Reorder the terms: -0.5102040815 + x = 2.526411919 Solving -0.5102040815 + x = 2.526411919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = 2.526411919 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 2.526411919 + 0.5102040815 x = 2.526411919 + 0.5102040815 Combine like terms: 2.526411919 + 0.5102040815 = 3.0366160005 x = 3.0366160005 Simplifying x = 3.0366160005Subproblem 2
x + -0.5102040815 = -2.526411919 Simplifying x + -0.5102040815 = -2.526411919 Reorder the terms: -0.5102040815 + x = -2.526411919 Solving -0.5102040815 + x = -2.526411919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = -2.526411919 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -2.526411919 + 0.5102040815 x = -2.526411919 + 0.5102040815 Combine like terms: -2.526411919 + 0.5102040815 = -2.0162078375 x = -2.0162078375 Simplifying x = -2.0162078375Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0366160005, -2.0162078375}
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