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Simplifying (3x + -4)(x + 3) = 15 Reorder the terms: (-4 + 3x)(x + 3) = 15 Reorder the terms: (-4 + 3x)(3 + x) = 15 Multiply (-4 + 3x) * (3 + x) (-4(3 + x) + 3x * (3 + x)) = 15 ((3 * -4 + x * -4) + 3x * (3 + x)) = 15 ((-12 + -4x) + 3x * (3 + x)) = 15 (-12 + -4x + (3 * 3x + x * 3x)) = 15 (-12 + -4x + (9x + 3x2)) = 15 Combine like terms: -4x + 9x = 5x (-12 + 5x + 3x2) = 15 Solving -12 + 5x + 3x2 = 15 Solving for variable 'x'. Reorder the terms: -12 + -15 + 5x + 3x2 = 15 + -15 Combine like terms: -12 + -15 = -27 -27 + 5x + 3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -27 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 1.666666667x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 1.666666667x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1.666666667x + x2 = 0 + 9 1.666666667x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 1.666666667x + x2 = 9 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 9 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 9 + 0.6944444447 Combine like terms: 9 + 0.6944444447 = 9.6944444447 0.6944444447 + 1.666666667x + x2 = 9.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 9.6944444447 Calculate the square root of the right side: 3.113590282 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.113590282 and -3.113590282.Subproblem 1
x + 0.8333333335 = 3.113590282 Simplifying x + 0.8333333335 = 3.113590282 Reorder the terms: 0.8333333335 + x = 3.113590282 Solving 0.8333333335 + x = 3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 3.113590282 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.113590282 + -0.8333333335 x = 3.113590282 + -0.8333333335 Combine like terms: 3.113590282 + -0.8333333335 = 2.2802569485 x = 2.2802569485 Simplifying x = 2.2802569485Subproblem 2
x + 0.8333333335 = -3.113590282 Simplifying x + 0.8333333335 = -3.113590282 Reorder the terms: 0.8333333335 + x = -3.113590282 Solving 0.8333333335 + x = -3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -3.113590282 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.113590282 + -0.8333333335 x = -3.113590282 + -0.8333333335 Combine like terms: -3.113590282 + -0.8333333335 = -3.9469236155 x = -3.9469236155 Simplifying x = -3.9469236155Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2802569485, -3.9469236155}
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