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Simplifying 20x2 + -16x + -6 = 0 Reorder the terms: -6 + -16x + 20x2 = 0 Solving -6 + -16x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -8x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -8x + 10x2)' equal to zero and attempt to solve: Simplifying -3 + -8x + 10x2 = 0 Solving -3 + -8x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -0.8x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.8x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.8x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.8x + x2 = 0.0 + 0.3 -0.8x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -0.8x + x2 = 0.3 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.3 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.3 + 0.16 Combine like terms: 0.3 + 0.16 = 0.46 0.16 + -0.8x + x2 = 0.46 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.46 Calculate the square root of the right side: 0.678232998 Break this problem into two subproblems by setting (x + -0.4) equal to 0.678232998 and -0.678232998.Subproblem 1
x + -0.4 = 0.678232998 Simplifying x + -0.4 = 0.678232998 Reorder the terms: -0.4 + x = 0.678232998 Solving -0.4 + x = 0.678232998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.678232998 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.678232998 + 0.4 x = 0.678232998 + 0.4 Combine like terms: 0.678232998 + 0.4 = 1.078232998 x = 1.078232998 Simplifying x = 1.078232998Subproblem 2
x + -0.4 = -0.678232998 Simplifying x + -0.4 = -0.678232998 Reorder the terms: -0.4 + x = -0.678232998 Solving -0.4 + x = -0.678232998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.678232998 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.678232998 + 0.4 x = -0.678232998 + 0.4 Combine like terms: -0.678232998 + 0.4 = -0.278232998 x = -0.278232998 Simplifying x = -0.278232998Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.078232998, -0.278232998}Solution
x = {1.078232998, -0.278232998}
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