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Simplifying x2 + -9.5x + -0.018796 = 0 Reorder the terms: -0.018796 + -9.5x + x2 = 0 Solving -0.018796 + -9.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.018796' to each side of the equation. -0.018796 + -9.5x + 0.018796 + x2 = 0 + 0.018796 Reorder the terms: -0.018796 + 0.018796 + -9.5x + x2 = 0 + 0.018796 Combine like terms: -0.018796 + 0.018796 = 0.000000 0.000000 + -9.5x + x2 = 0 + 0.018796 -9.5x + x2 = 0 + 0.018796 Combine like terms: 0 + 0.018796 = 0.018796 -9.5x + x2 = 0.018796 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 = 0.018796 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 0.018796 + 22.5625 Combine like terms: 0.018796 + 22.5625 = 22.581296 22.5625 + -9.5x + x2 = 22.581296 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 22.581296 Calculate the square root of the right side: 4.751978114 Break this problem into two subproblems by setting (x + -4.75) equal to 4.751978114 and -4.751978114.Subproblem 1
x + -4.75 = 4.751978114 Simplifying x + -4.75 = 4.751978114 Reorder the terms: -4.75 + x = 4.751978114 Solving -4.75 + x = 4.751978114 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 = 4.751978114 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.751978114 + 4.75 x = 4.751978114 + 4.75 Combine like terms: 4.751978114 + 4.75 = 9.501978114 x = 9.501978114 Simplifying x = 9.501978114Subproblem 2
x + -4.75 = -4.751978114 Simplifying x + -4.75 = -4.751978114 Reorder the terms: -4.75 + x = -4.751978114 Solving -4.75 + x = -4.751978114 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 = -4.751978114 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.751978114 + 4.75 x = -4.751978114 + 4.75 Combine like terms: -4.751978114 + 4.75 = -0.001978114 x = -0.001978114 Simplifying x = -0.001978114Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.501978114, -0.001978114}
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