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Simplifying 96x2 + -58x + -40 = 0 Reorder the terms: -40 + -58x + 96x2 = 0 Solving -40 + -58x + 96x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -29x + 48x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + -29x + 48x2)' equal to zero and attempt to solve: Simplifying -20 + -29x + 48x2 = 0 Solving -20 + -29x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.4166666667 + -0.6041666667x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.6041666667x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.6041666667x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.6041666667x + x2 = 0 + 0.4166666667 -0.6041666667x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.6041666667x + x2 = 0.4166666667 The x term is -0.6041666667x. Take half its coefficient (-0.3020833334). Square it (0.09125434032) and add it to both sides. Add '0.09125434032' to each side of the equation. -0.6041666667x + 0.09125434032 + x2 = 0.4166666667 + 0.09125434032 Reorder the terms: 0.09125434032 + -0.6041666667x + x2 = 0.4166666667 + 0.09125434032 Combine like terms: 0.4166666667 + 0.09125434032 = 0.50792100702 0.09125434032 + -0.6041666667x + x2 = 0.50792100702 Factor a perfect square on the left side: (x + -0.3020833334)(x + -0.3020833334) = 0.50792100702 Calculate the square root of the right side: 0.71268577 Break this problem into two subproblems by setting (x + -0.3020833334) equal to 0.71268577 and -0.71268577.Subproblem 1
x + -0.3020833334 = 0.71268577 Simplifying x + -0.3020833334 = 0.71268577 Reorder the terms: -0.3020833334 + x = 0.71268577 Solving -0.3020833334 + x = 0.71268577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3020833334' to each side of the equation. -0.3020833334 + 0.3020833334 + x = 0.71268577 + 0.3020833334 Combine like terms: -0.3020833334 + 0.3020833334 = 0.0000000000 0.0000000000 + x = 0.71268577 + 0.3020833334 x = 0.71268577 + 0.3020833334 Combine like terms: 0.71268577 + 0.3020833334 = 1.0147691034 x = 1.0147691034 Simplifying x = 1.0147691034Subproblem 2
x + -0.3020833334 = -0.71268577 Simplifying x + -0.3020833334 = -0.71268577 Reorder the terms: -0.3020833334 + x = -0.71268577 Solving -0.3020833334 + x = -0.71268577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3020833334' to each side of the equation. -0.3020833334 + 0.3020833334 + x = -0.71268577 + 0.3020833334 Combine like terms: -0.3020833334 + 0.3020833334 = 0.0000000000 0.0000000000 + x = -0.71268577 + 0.3020833334 x = -0.71268577 + 0.3020833334 Combine like terms: -0.71268577 + 0.3020833334 = -0.4106024366 x = -0.4106024366 Simplifying x = -0.4106024366Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0147691034, -0.4106024366}Solution
x = {1.0147691034, -0.4106024366}
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