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Simplifying (5x + 9)(12 + 2x) = 33 Reorder the terms: (9 + 5x)(12 + 2x) = 33 Multiply (9 + 5x) * (12 + 2x) (9(12 + 2x) + 5x * (12 + 2x)) = 33 ((12 * 9 + 2x * 9) + 5x * (12 + 2x)) = 33 ((108 + 18x) + 5x * (12 + 2x)) = 33 (108 + 18x + (12 * 5x + 2x * 5x)) = 33 (108 + 18x + (60x + 10x2)) = 33 Combine like terms: 18x + 60x = 78x (108 + 78x + 10x2) = 33 Solving 108 + 78x + 10x2 = 33 Solving for variable 'x'. Reorder the terms: 108 + -33 + 78x + 10x2 = 33 + -33 Combine like terms: 108 + -33 = 75 75 + 78x + 10x2 = 33 + -33 Combine like terms: 33 + -33 = 0 75 + 78x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 7.5 + 7.8x + x2 = 0.0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 7.8x + -7.5 + x2 = 0.0 + -7.5 Reorder the terms: 7.5 + -7.5 + 7.8x + x2 = 0.0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 7.8x + x2 = 0.0 + -7.5 7.8x + x2 = 0.0 + -7.5 Combine like terms: 0.0 + -7.5 = -7.5 7.8x + x2 = -7.5 The x term is 7.8x. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8x + 15.21 + x2 = -7.5 + 15.21 Reorder the terms: 15.21 + 7.8x + x2 = -7.5 + 15.21 Combine like terms: -7.5 + 15.21 = 7.71 15.21 + 7.8x + x2 = 7.71 Factor a perfect square on the left side: (x + 3.9)(x + 3.9) = 7.71 Calculate the square root of the right side: 2.776688675 Break this problem into two subproblems by setting (x + 3.9) equal to 2.776688675 and -2.776688675.Subproblem 1
x + 3.9 = 2.776688675 Simplifying x + 3.9 = 2.776688675 Reorder the terms: 3.9 + x = 2.776688675 Solving 3.9 + x = 2.776688675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = 2.776688675 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = 2.776688675 + -3.9 x = 2.776688675 + -3.9 Combine like terms: 2.776688675 + -3.9 = -1.123311325 x = -1.123311325 Simplifying x = -1.123311325Subproblem 2
x + 3.9 = -2.776688675 Simplifying x + 3.9 = -2.776688675 Reorder the terms: 3.9 + x = -2.776688675 Solving 3.9 + x = -2.776688675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = -2.776688675 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = -2.776688675 + -3.9 x = -2.776688675 + -3.9 Combine like terms: -2.776688675 + -3.9 = -6.676688675 x = -6.676688675 Simplifying x = -6.676688675Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.123311325, -6.676688675}
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