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Simplifying (x + 5)(x + 3) + -6 = 0 Reorder the terms: (5 + x)(x + 3) + -6 = 0 Reorder the terms: (5 + x)(3 + x) + -6 = 0 Multiply (5 + x) * (3 + x) (5(3 + x) + x(3 + x)) + -6 = 0 ((3 * 5 + x * 5) + x(3 + x)) + -6 = 0 ((15 + 5x) + x(3 + x)) + -6 = 0 (15 + 5x + (3 * x + x * x)) + -6 = 0 (15 + 5x + (3x + x2)) + -6 = 0 Combine like terms: 5x + 3x = 8x (15 + 8x + x2) + -6 = 0 Reorder the terms: 15 + -6 + 8x + x2 = 0 Combine like terms: 15 + -6 = 9 9 + 8x + x2 = 0 Solving 9 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 8x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8x + x2 = 0 + -9 8x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 8x + x2 = -9 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -9 + 16 Reorder the terms: 16 + 8x + x2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8x + x2 = 7 Factor a perfect square on the left side: (x + 4)(x + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 4 = 2.645751311 Simplifying x + 4 = 2.645751311 Reorder the terms: 4 + x = 2.645751311 Solving 4 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.645751311 + -4 x = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 x = -1.354248689 Simplifying x = -1.354248689Subproblem 2
x + 4 = -2.645751311 Simplifying x + 4 = -2.645751311 Reorder the terms: 4 + x = -2.645751311 Solving 4 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.645751311 + -4 x = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 x = -6.645751311 Simplifying x = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.354248689, -6.645751311}
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