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Simplifying -24x2 + 10x + 12 = 0 Reorder the terms: 12 + 10x + -24x2 = 0 Solving 12 + 10x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 5x + -12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 5x + -12x2)' equal to zero and attempt to solve: Simplifying 6 + 5x + -12x2 = 0 Solving 6 + 5x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.5 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.4166666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.4166666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.4166666667x + x2 = 0 + 0.5 -0.4166666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.4166666667x + x2 = 0.5 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 = 0.5 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 0.5 + 0.04340277781 Combine like terms: 0.5 + 0.04340277781 = 0.54340277781 0.04340277781 + -0.4166666667x + x2 = 0.54340277781 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 0.54340277781 Calculate the square root of the right side: 0.737158584 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 0.737158584 and -0.737158584.Subproblem 1
x + -0.2083333334 = 0.737158584 Simplifying x + -0.2083333334 = 0.737158584 Reorder the terms: -0.2083333334 + x = 0.737158584 Solving -0.2083333334 + x = 0.737158584 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 = 0.737158584 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 0.737158584 + 0.2083333334 x = 0.737158584 + 0.2083333334 Combine like terms: 0.737158584 + 0.2083333334 = 0.9454919174 x = 0.9454919174 Simplifying x = 0.9454919174Subproblem 2
x + -0.2083333334 = -0.737158584 Simplifying x + -0.2083333334 = -0.737158584 Reorder the terms: -0.2083333334 + x = -0.737158584 Solving -0.2083333334 + x = -0.737158584 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 = -0.737158584 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -0.737158584 + 0.2083333334 x = -0.737158584 + 0.2083333334 Combine like terms: -0.737158584 + 0.2083333334 = -0.5288252506 x = -0.5288252506 Simplifying x = -0.5288252506Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9454919174, -0.5288252506}Solution
x = {0.9454919174, -0.5288252506}
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