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Simplifying 20x2 + -30x + -6 = 0 Reorder the terms: -6 + -30x + 20x2 = 0 Solving -6 + -30x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -15x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -15x + 10x2)' equal to zero and attempt to solve: Simplifying -3 + -15x + 10x2 = 0 Solving -3 + -15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -1.5x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -1.5x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.5x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.5x + x2 = 0.0 + 0.3 -1.5x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -1.5x + x2 = 0.3 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.3 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.3 + 0.5625 Combine like terms: 0.3 + 0.5625 = 0.8625 0.5625 + -1.5x + x2 = 0.8625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.8625 Calculate the square root of the right side: 0.928708781 Break this problem into two subproblems by setting (x + -0.75) equal to 0.928708781 and -0.928708781.Subproblem 1
x + -0.75 = 0.928708781 Simplifying x + -0.75 = 0.928708781 Reorder the terms: -0.75 + x = 0.928708781 Solving -0.75 + x = 0.928708781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.928708781 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.928708781 + 0.75 x = 0.928708781 + 0.75 Combine like terms: 0.928708781 + 0.75 = 1.678708781 x = 1.678708781 Simplifying x = 1.678708781Subproblem 2
x + -0.75 = -0.928708781 Simplifying x + -0.75 = -0.928708781 Reorder the terms: -0.75 + x = -0.928708781 Solving -0.75 + x = -0.928708781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.928708781 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.928708781 + 0.75 x = -0.928708781 + 0.75 Combine like terms: -0.928708781 + 0.75 = -0.178708781 x = -0.178708781 Simplifying x = -0.178708781Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.678708781, -0.178708781}Solution
x = {1.678708781, -0.178708781}
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