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Simplifying (3x + 3)(x + -6) = 24x + -118 Reorder the terms: (3 + 3x)(x + -6) = 24x + -118 Reorder the terms: (3 + 3x)(-6 + x) = 24x + -118 Multiply (3 + 3x) * (-6 + x) (3(-6 + x) + 3x * (-6 + x)) = 24x + -118 ((-6 * 3 + x * 3) + 3x * (-6 + x)) = 24x + -118 ((-18 + 3x) + 3x * (-6 + x)) = 24x + -118 (-18 + 3x + (-6 * 3x + x * 3x)) = 24x + -118 (-18 + 3x + (-18x + 3x2)) = 24x + -118 Combine like terms: 3x + -18x = -15x (-18 + -15x + 3x2) = 24x + -118 Reorder the terms: -18 + -15x + 3x2 = -118 + 24x Solving -18 + -15x + 3x2 = -118 + 24x Solving for variable 'x'. Reorder the terms: -18 + 118 + -15x + -24x + 3x2 = -118 + 24x + 118 + -24x Combine like terms: -18 + 118 = 100 100 + -15x + -24x + 3x2 = -118 + 24x + 118 + -24x Combine like terms: -15x + -24x = -39x 100 + -39x + 3x2 = -118 + 24x + 118 + -24x Reorder the terms: 100 + -39x + 3x2 = -118 + 118 + 24x + -24x Combine like terms: -118 + 118 = 0 100 + -39x + 3x2 = 0 + 24x + -24x 100 + -39x + 3x2 = 24x + -24x Combine like terms: 24x + -24x = 0 100 + -39x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 33.33333333 + -13x + x2 = 0 Move the constant term to the right: Add '-33.33333333' to each side of the equation. 33.33333333 + -13x + -33.33333333 + x2 = 0 + -33.33333333 Reorder the terms: 33.33333333 + -33.33333333 + -13x + x2 = 0 + -33.33333333 Combine like terms: 33.33333333 + -33.33333333 = 0.00000000 0.00000000 + -13x + x2 = 0 + -33.33333333 -13x + x2 = 0 + -33.33333333 Combine like terms: 0 + -33.33333333 = -33.33333333 -13x + x2 = -33.33333333 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -33.33333333 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -33.33333333 + 42.25 Combine like terms: -33.33333333 + 42.25 = 8.91666667 42.25 + -13x + x2 = 8.91666667 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 8.91666667 Calculate the square root of the right side: 2.986078812 Break this problem into two subproblems by setting (x + -6.5) equal to 2.986078812 and -2.986078812.Subproblem 1
x + -6.5 = 2.986078812 Simplifying x + -6.5 = 2.986078812 Reorder the terms: -6.5 + x = 2.986078812 Solving -6.5 + x = 2.986078812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 2.986078812 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 2.986078812 + 6.5 x = 2.986078812 + 6.5 Combine like terms: 2.986078812 + 6.5 = 9.486078812 x = 9.486078812 Simplifying x = 9.486078812Subproblem 2
x + -6.5 = -2.986078812 Simplifying x + -6.5 = -2.986078812 Reorder the terms: -6.5 + x = -2.986078812 Solving -6.5 + x = -2.986078812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -2.986078812 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -2.986078812 + 6.5 x = -2.986078812 + 6.5 Combine like terms: -2.986078812 + 6.5 = 3.513921188 x = 3.513921188 Simplifying x = 3.513921188Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.486078812, 3.513921188}
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