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Simplifying 50 + -1x = 60 + 18x + 2x2 Solving 50 + -1x = 60 + 18x + 2x2 Solving for variable 'x'. Reorder the terms: 50 + -60 + -1x + -18x + -2x2 = 60 + 18x + 2x2 + -60 + -18x + -2x2 Combine like terms: 50 + -60 = -10 -10 + -1x + -18x + -2x2 = 60 + 18x + 2x2 + -60 + -18x + -2x2 Combine like terms: -1x + -18x = -19x -10 + -19x + -2x2 = 60 + 18x + 2x2 + -60 + -18x + -2x2 Reorder the terms: -10 + -19x + -2x2 = 60 + -60 + 18x + -18x + 2x2 + -2x2 Combine like terms: 60 + -60 = 0 -10 + -19x + -2x2 = 0 + 18x + -18x + 2x2 + -2x2 -10 + -19x + -2x2 = 18x + -18x + 2x2 + -2x2 Combine like terms: 18x + -18x = 0 -10 + -19x + -2x2 = 0 + 2x2 + -2x2 -10 + -19x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -10 + -19x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 19x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 19x + 2x2)' equal to zero and attempt to solve: Simplifying 10 + 19x + 2x2 = 0 Solving 10 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + 9.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 9.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 9.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9.5x + x2 = 0 + -5 9.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 9.5x + x2 = -5 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = -5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -5 + 22.5625 Combine like terms: -5 + 22.5625 = 17.5625 22.5625 + 9.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + 4.75) equal to 4.190763654 and -4.190763654.Subproblem 1
x + 4.75 = 4.190763654 Simplifying x + 4.75 = 4.190763654 Reorder the terms: 4.75 + x = 4.190763654 Solving 4.75 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 4.190763654 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 4.190763654 + -4.75 x = 4.190763654 + -4.75 Combine like terms: 4.190763654 + -4.75 = -0.559236346 x = -0.559236346 Simplifying x = -0.559236346Subproblem 2
x + 4.75 = -4.190763654 Simplifying x + 4.75 = -4.190763654 Reorder the terms: 4.75 + x = -4.190763654 Solving 4.75 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -4.190763654 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -4.190763654 + -4.75 x = -4.190763654 + -4.75 Combine like terms: -4.190763654 + -4.75 = -8.940763654 x = -8.940763654 Simplifying x = -8.940763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.559236346, -8.940763654}Solution
x = {-0.559236346, -8.940763654}
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