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Simplifying (x + -6) * 6x + -48 = 8 Reorder the terms: (-6 + x) * 6x + -48 = 8 Reorder the terms for easier multiplication: 6x(-6 + x) + -48 = 8 (-6 * 6x + x * 6x) + -48 = 8 (-36x + 6x2) + -48 = 8 Reorder the terms: -48 + -36x + 6x2 = 8 Solving -48 + -36x + 6x2 = 8 Solving for variable 'x'. Reorder the terms: -48 + -8 + -36x + 6x2 = 8 + -8 Combine like terms: -48 + -8 = -56 -56 + -36x + 6x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -56 + -36x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -18x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -18x + 3x2)' equal to zero and attempt to solve: Simplifying -28 + -18x + 3x2 = 0 Solving -28 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -6x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -6x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -6x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -6x + x2 = 0 + 9.333333333 -6x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -6x + x2 = 9.333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 9.333333333 + 9 Reorder the terms: 9 + -6x + x2 = 9.333333333 + 9 Combine like terms: 9.333333333 + 9 = 18.333333333 9 + -6x + x2 = 18.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 18.333333333 Calculate the square root of the right side: 4.281744193 Break this problem into two subproblems by setting (x + -3) equal to 4.281744193 and -4.281744193.Subproblem 1
x + -3 = 4.281744193 Simplifying x + -3 = 4.281744193 Reorder the terms: -3 + x = 4.281744193 Solving -3 + x = 4.281744193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.281744193 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.281744193 + 3 x = 4.281744193 + 3 Combine like terms: 4.281744193 + 3 = 7.281744193 x = 7.281744193 Simplifying x = 7.281744193Subproblem 2
x + -3 = -4.281744193 Simplifying x + -3 = -4.281744193 Reorder the terms: -3 + x = -4.281744193 Solving -3 + x = -4.281744193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.281744193 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.281744193 + 3 x = -4.281744193 + 3 Combine like terms: -4.281744193 + 3 = -1.281744193 x = -1.281744193 Simplifying x = -1.281744193Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.281744193, -1.281744193}Solution
x = {7.281744193, -1.281744193}
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