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Simplifying -20x2 + -25x + -6 = 0 Reorder the terms: -6 + -25x + -20x2 = 0 Solving -6 + -25x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 25x + 20x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 25x + 20x2)' equal to zero and attempt to solve: Simplifying 6 + 25x + 20x2 = 0 Solving 6 + 25x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.3 + 1.25x + x2 = 0.0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + 1.25x + -0.3 + x2 = 0.0 + -0.3 Reorder the terms: 0.3 + -0.3 + 1.25x + x2 = 0.0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + 1.25x + x2 = 0.0 + -0.3 1.25x + x2 = 0.0 + -0.3 Combine like terms: 0.0 + -0.3 = -0.3 1.25x + x2 = -0.3 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -0.3 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -0.3 + 0.390625 Combine like terms: -0.3 + 0.390625 = 0.090625 0.390625 + 1.25x + x2 = 0.090625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.090625 Calculate the square root of the right side: 0.301039864 Break this problem into two subproblems by setting (x + 0.625) equal to 0.301039864 and -0.301039864.Subproblem 1
x + 0.625 = 0.301039864 Simplifying x + 0.625 = 0.301039864 Reorder the terms: 0.625 + x = 0.301039864 Solving 0.625 + x = 0.301039864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.301039864 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.301039864 + -0.625 x = 0.301039864 + -0.625 Combine like terms: 0.301039864 + -0.625 = -0.323960136 x = -0.323960136 Simplifying x = -0.323960136Subproblem 2
x + 0.625 = -0.301039864 Simplifying x + 0.625 = -0.301039864 Reorder the terms: 0.625 + x = -0.301039864 Solving 0.625 + x = -0.301039864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.301039864 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.301039864 + -0.625 x = -0.301039864 + -0.625 Combine like terms: -0.301039864 + -0.625 = -0.926039864 x = -0.926039864 Simplifying x = -0.926039864Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.323960136, -0.926039864}Solution
x = {-0.323960136, -0.926039864}
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