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Simplifying (x + -3)(3x) = 27x + 99 Reorder the terms: (-3 + x)(3x) = 27x + 99 Remove parenthesis around (3x) (-3 + x) * 3x = 27x + 99 Reorder the terms for easier multiplication: 3x(-3 + x) = 27x + 99 (-3 * 3x + x * 3x) = 27x + 99 (-9x + 3x2) = 27x + 99 Reorder the terms: -9x + 3x2 = 99 + 27x Solving -9x + 3x2 = 99 + 27x Solving for variable 'x'. Reorder the terms: -99 + -9x + -27x + 3x2 = 99 + 27x + -99 + -27x Combine like terms: -9x + -27x = -36x -99 + -36x + 3x2 = 99 + 27x + -99 + -27x Reorder the terms: -99 + -36x + 3x2 = 99 + -99 + 27x + -27x Combine like terms: 99 + -99 = 0 -99 + -36x + 3x2 = 0 + 27x + -27x -99 + -36x + 3x2 = 27x + -27x Combine like terms: 27x + -27x = 0 -99 + -36x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-33 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-33 + -12x + x2)' equal to zero and attempt to solve: Simplifying -33 + -12x + x2 = 0 Solving -33 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -12x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -12x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -12x + x2 = 0 + 33 -12x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -12x + x2 = 33 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 33 + 36 Reorder the terms: 36 + -12x + x2 = 33 + 36 Combine like terms: 33 + 36 = 69 36 + -12x + x2 = 69 Factor a perfect square on the left side: (x + -6)(x + -6) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + -6) equal to 8.306623863 and -8.306623863.Subproblem 1
x + -6 = 8.306623863 Simplifying x + -6 = 8.306623863 Reorder the terms: -6 + x = 8.306623863 Solving -6 + x = 8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.306623863 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.306623863 + 6 x = 8.306623863 + 6 Combine like terms: 8.306623863 + 6 = 14.306623863 x = 14.306623863 Simplifying x = 14.306623863Subproblem 2
x + -6 = -8.306623863 Simplifying x + -6 = -8.306623863 Reorder the terms: -6 + x = -8.306623863 Solving -6 + x = -8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.306623863 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.306623863 + 6 x = -8.306623863 + 6 Combine like terms: -8.306623863 + 6 = -2.306623863 x = -2.306623863 Simplifying x = -2.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.306623863, -2.306623863}Solution
x = {14.306623863, -2.306623863}
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