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Simplifying 8x2 + -36x + -24 = 0 Reorder the terms: -24 + -36x + 8x2 = 0 Solving -24 + -36x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -9x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying -6 + -9x + 2x2 = 0 Solving -6 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -4.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -4.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4.5x + x2 = 0 + 3 -4.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4.5x + x2 = 3 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 3 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 3 + 5.0625 Combine like terms: 3 + 5.0625 = 8.0625 5.0625 + -4.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -2.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -2.25 = 2.839454173 Simplifying x + -2.25 = 2.839454173 Reorder the terms: -2.25 + x = 2.839454173 Solving -2.25 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.839454173 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.839454173 + 2.25 x = 2.839454173 + 2.25 Combine like terms: 2.839454173 + 2.25 = 5.089454173 x = 5.089454173 Simplifying x = 5.089454173Subproblem 2
x + -2.25 = -2.839454173 Simplifying x + -2.25 = -2.839454173 Reorder the terms: -2.25 + x = -2.839454173 Solving -2.25 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.839454173 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.839454173 + 2.25 x = -2.839454173 + 2.25 Combine like terms: -2.839454173 + 2.25 = -0.589454173 x = -0.589454173 Simplifying x = -0.589454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.089454173, -0.589454173}Solution
x = {5.089454173, -0.589454173}
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