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Simplifying 24x2 + -3x + -18 = 0 Reorder the terms: -18 + -3x + 24x2 = 0 Solving -18 + -3x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + -1x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -1x + 8x2)' equal to zero and attempt to solve: Simplifying -6 + -1x + 8x2 = 0 Solving -6 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.125x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.125x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.125x + x2 = 0 + 0.75 -0.125x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.125x + x2 = 0.75 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 0.75 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.75 + 0.00390625 Combine like terms: 0.75 + 0.00390625 = 0.75390625 0.00390625 + -0.125x + x2 = 0.75390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.75390625 Calculate the square root of the right side: 0.868277749 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.868277749 and -0.868277749.Subproblem 1
x + -0.0625 = 0.868277749 Simplifying x + -0.0625 = 0.868277749 Reorder the terms: -0.0625 + x = 0.868277749 Solving -0.0625 + x = 0.868277749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.868277749 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.868277749 + 0.0625 x = 0.868277749 + 0.0625 Combine like terms: 0.868277749 + 0.0625 = 0.930777749 x = 0.930777749 Simplifying x = 0.930777749Subproblem 2
x + -0.0625 = -0.868277749 Simplifying x + -0.0625 = -0.868277749 Reorder the terms: -0.0625 + x = -0.868277749 Solving -0.0625 + x = -0.868277749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.868277749 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.868277749 + 0.0625 x = -0.868277749 + 0.0625 Combine like terms: -0.868277749 + 0.0625 = -0.805777749 x = -0.805777749 Simplifying x = -0.805777749Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.930777749, -0.805777749}Solution
x = {0.930777749, -0.805777749}
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