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Simplifying 24x2 + 10x + -24 = 0 Reorder the terms: -24 + 10x + 24x2 = 0 Solving -24 + 10x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 5x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 5x + 12x2)' equal to zero and attempt to solve: Simplifying -12 + 5x + 12x2 = 0 Solving -12 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.4166666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.4166666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.4166666667x + x2 = 0 + 1 0.4166666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.4166666667x + x2 = 1 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 = 1 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 1 + 0.04340277781 Combine like terms: 1 + 0.04340277781 = 1.04340277781 0.04340277781 + 0.4166666667x + x2 = 1.04340277781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 1.04340277781 Calculate the square root of the right side: 1.021470889 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 1.021470889 and -1.021470889.Subproblem 1
x + 0.2083333334 = 1.021470889 Simplifying x + 0.2083333334 = 1.021470889 Reorder the terms: 0.2083333334 + x = 1.021470889 Solving 0.2083333334 + x = 1.021470889 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 = 1.021470889 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 1.021470889 + -0.2083333334 x = 1.021470889 + -0.2083333334 Combine like terms: 1.021470889 + -0.2083333334 = 0.8131375556 x = 0.8131375556 Simplifying x = 0.8131375556Subproblem 2
x + 0.2083333334 = -1.021470889 Simplifying x + 0.2083333334 = -1.021470889 Reorder the terms: 0.2083333334 + x = -1.021470889 Solving 0.2083333334 + x = -1.021470889 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 = -1.021470889 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -1.021470889 + -0.2083333334 x = -1.021470889 + -0.2083333334 Combine like terms: -1.021470889 + -0.2083333334 = -1.2298042224 x = -1.2298042224 Simplifying x = -1.2298042224Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8131375556, -1.2298042224}Solution
x = {0.8131375556, -1.2298042224}
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