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Simplifying 80x2 + -48x + -38 = 0 Reorder the terms: -38 + -48x + 80x2 = 0 Solving -38 + -48x + 80x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + -24x + 40x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + -24x + 40x2)' equal to zero and attempt to solve: Simplifying -19 + -24x + 40x2 = 0 Solving -19 + -24x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.475 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '0.475' to each side of the equation. -0.475 + -0.6x + 0.475 + x2 = 0.0 + 0.475 Reorder the terms: -0.475 + 0.475 + -0.6x + x2 = 0.0 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + -0.6x + x2 = 0.0 + 0.475 -0.6x + x2 = 0.0 + 0.475 Combine like terms: 0.0 + 0.475 = 0.475 -0.6x + x2 = 0.475 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.475 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.475 + 0.09 Combine like terms: 0.475 + 0.09 = 0.565 0.09 + -0.6x + x2 = 0.565 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.565 Calculate the square root of the right side: 0.751664819 Break this problem into two subproblems by setting (x + -0.3) equal to 0.751664819 and -0.751664819.Subproblem 1
x + -0.3 = 0.751664819 Simplifying x + -0.3 = 0.751664819 Reorder the terms: -0.3 + x = 0.751664819 Solving -0.3 + x = 0.751664819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.751664819 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.751664819 + 0.3 x = 0.751664819 + 0.3 Combine like terms: 0.751664819 + 0.3 = 1.051664819 x = 1.051664819 Simplifying x = 1.051664819Subproblem 2
x + -0.3 = -0.751664819 Simplifying x + -0.3 = -0.751664819 Reorder the terms: -0.3 + x = -0.751664819 Solving -0.3 + x = -0.751664819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.751664819 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.751664819 + 0.3 x = -0.751664819 + 0.3 Combine like terms: -0.751664819 + 0.3 = -0.451664819 x = -0.451664819 Simplifying x = -0.451664819Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.051664819, -0.451664819}Solution
x = {1.051664819, -0.451664819}
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