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Simplifying 80x2 + -20x + -6 = 0 Reorder the terms: -6 + -20x + 80x2 = 0 Solving -6 + -20x + 80x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -10x + 40x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -10x + 40x2)' equal to zero and attempt to solve: Simplifying -3 + -10x + 40x2 = 0 Solving -3 + -10x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.075 + -0.25x + x2 = 0.0 Move the constant term to the right: Add '0.075' to each side of the equation. -0.075 + -0.25x + 0.075 + x2 = 0.0 + 0.075 Reorder the terms: -0.075 + 0.075 + -0.25x + x2 = 0.0 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + -0.25x + x2 = 0.0 + 0.075 -0.25x + x2 = 0.0 + 0.075 Combine like terms: 0.0 + 0.075 = 0.075 -0.25x + x2 = 0.075 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.075 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.075 + 0.015625 Combine like terms: 0.075 + 0.015625 = 0.090625 0.015625 + -0.25x + x2 = 0.090625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.090625 Calculate the square root of the right side: 0.301039864 Break this problem into two subproblems by setting (x + -0.125) equal to 0.301039864 and -0.301039864.Subproblem 1
x + -0.125 = 0.301039864 Simplifying x + -0.125 = 0.301039864 Reorder the terms: -0.125 + x = 0.301039864 Solving -0.125 + x = 0.301039864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.301039864 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.301039864 + 0.125 x = 0.301039864 + 0.125 Combine like terms: 0.301039864 + 0.125 = 0.426039864 x = 0.426039864 Simplifying x = 0.426039864Subproblem 2
x + -0.125 = -0.301039864 Simplifying x + -0.125 = -0.301039864 Reorder the terms: -0.125 + x = -0.301039864 Solving -0.125 + x = -0.301039864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.301039864 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.301039864 + 0.125 x = -0.301039864 + 0.125 Combine like terms: -0.301039864 + 0.125 = -0.176039864 x = -0.176039864 Simplifying x = -0.176039864Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.426039864, -0.176039864}Solution
x = {0.426039864, -0.176039864}
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