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Simplifying 0 = 6(x2 + -18x) + -24 Reorder the terms: 0 = 6(-18x + x2) + -24 0 = (-18x * 6 + x2 * 6) + -24 0 = (-108x + 6x2) + -24 Reorder the terms: 0 = -24 + -108x + 6x2 Solving 0 = -24 + -108x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + 108x + -6x2 = -24 + -108x + 6x2 + 24 + 108x + -6x2 Reorder the terms: 24 + 108x + -6x2 = -24 + 24 + -108x + 108x + 6x2 + -6x2 Combine like terms: -24 + 24 = 0 24 + 108x + -6x2 = 0 + -108x + 108x + 6x2 + -6x2 24 + 108x + -6x2 = -108x + 108x + 6x2 + -6x2 Combine like terms: -108x + 108x = 0 24 + 108x + -6x2 = 0 + 6x2 + -6x2 24 + 108x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 24 + 108x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(4 + 18x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + 18x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + 18x + -1x2 = 0 Solving 4 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -18x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -18x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -18x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -18x + x2 = 0 + 4 -18x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -18x + x2 = 4 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 4 + 81 Reorder the terms: 81 + -18x + x2 = 4 + 81 Combine like terms: 4 + 81 = 85 81 + -18x + x2 = 85 Factor a perfect square on the left side: (x + -9)(x + -9) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + -9) equal to 9.219544457 and -9.219544457.Subproblem 1
x + -9 = 9.219544457 Simplifying x + -9 = 9.219544457 Reorder the terms: -9 + x = 9.219544457 Solving -9 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.219544457 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.219544457 + 9 x = 9.219544457 + 9 Combine like terms: 9.219544457 + 9 = 18.219544457 x = 18.219544457 Simplifying x = 18.219544457Subproblem 2
x + -9 = -9.219544457 Simplifying x + -9 = -9.219544457 Reorder the terms: -9 + x = -9.219544457 Solving -9 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.219544457 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.219544457 + 9 x = -9.219544457 + 9 Combine like terms: -9.219544457 + 9 = -0.219544457 x = -0.219544457 Simplifying x = -0.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.219544457, -0.219544457}Solution
x = {18.219544457, -0.219544457}
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