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Simplifying 24x2 + -27x + 6 = 0 Reorder the terms: 6 + -27x + 24x2 = 0 Solving 6 + -27x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -9x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -9x + 8x2)' equal to zero and attempt to solve: Simplifying 2 + -9x + 8x2 = 0 Solving 2 + -9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -1.125x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.125x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.125x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.125x + x2 = 0 + -0.25 -1.125x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.125x + x2 = -0.25 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = -0.25 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = -0.25 + 0.31640625 Combine like terms: -0.25 + 0.31640625 = 0.06640625 0.31640625 + -1.125x + x2 = 0.06640625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (x + -0.5625) equal to 0.257694102 and -0.257694102.Subproblem 1
x + -0.5625 = 0.257694102 Simplifying x + -0.5625 = 0.257694102 Reorder the terms: -0.5625 + x = 0.257694102 Solving -0.5625 + x = 0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.257694102 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.257694102 + 0.5625 x = 0.257694102 + 0.5625 Combine like terms: 0.257694102 + 0.5625 = 0.820194102 x = 0.820194102 Simplifying x = 0.820194102Subproblem 2
x + -0.5625 = -0.257694102 Simplifying x + -0.5625 = -0.257694102 Reorder the terms: -0.5625 + x = -0.257694102 Solving -0.5625 + x = -0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.257694102 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.257694102 + 0.5625 x = -0.257694102 + 0.5625 Combine like terms: -0.257694102 + 0.5625 = 0.304805898 x = 0.304805898 Simplifying x = 0.304805898Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.820194102, 0.304805898}Solution
x = {0.820194102, 0.304805898}
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