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Simplifying 24x2 + -10x + -8 = 0 Reorder the terms: -8 + -10x + 24x2 = 0 Solving -8 + -10x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -5x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5x + 12x2)' equal to zero and attempt to solve: Simplifying -4 + -5x + 12x2 = 0 Solving -4 + -5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.3333333333 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.4166666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.4166666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.4166666667x + x2 = 0 + 0.3333333333 -0.4166666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.4166666667x + x2 = 0.3333333333 The x term is -0.4166666667x. Take half its coefficient (-0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. -0.4166666667x + 0.04340277781 + x2 = 0.3333333333 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 0.3333333333 + 0.04340277781 Combine like terms: 0.3333333333 + 0.04340277781 = 0.37673611111 0.04340277781 + -0.4166666667x + x2 = 0.37673611111 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 0.37673611111 Calculate the square root of the right side: 0.613788328 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 0.613788328 and -0.613788328.Subproblem 1
x + -0.2083333334 = 0.613788328 Simplifying x + -0.2083333334 = 0.613788328 Reorder the terms: -0.2083333334 + x = 0.613788328 Solving -0.2083333334 + x = 0.613788328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = 0.613788328 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 0.613788328 + 0.2083333334 x = 0.613788328 + 0.2083333334 Combine like terms: 0.613788328 + 0.2083333334 = 0.8221216614 x = 0.8221216614 Simplifying x = 0.8221216614Subproblem 2
x + -0.2083333334 = -0.613788328 Simplifying x + -0.2083333334 = -0.613788328 Reorder the terms: -0.2083333334 + x = -0.613788328 Solving -0.2083333334 + x = -0.613788328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = -0.613788328 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -0.613788328 + 0.2083333334 x = -0.613788328 + 0.2083333334 Combine like terms: -0.613788328 + 0.2083333334 = -0.4054549946 x = -0.4054549946 Simplifying x = -0.4054549946Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8221216614, -0.4054549946}Solution
x = {0.8221216614, -0.4054549946}
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