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Simplifying (x + 3)(x + 5) + -100 = 0 Reorder the terms: (3 + x)(x + 5) + -100 = 0 Reorder the terms: (3 + x)(5 + x) + -100 = 0 Multiply (3 + x) * (5 + x) (3(5 + x) + x(5 + x)) + -100 = 0 ((5 * 3 + x * 3) + x(5 + x)) + -100 = 0 ((15 + 3x) + x(5 + x)) + -100 = 0 (15 + 3x + (5 * x + x * x)) + -100 = 0 (15 + 3x + (5x + x2)) + -100 = 0 Combine like terms: 3x + 5x = 8x (15 + 8x + x2) + -100 = 0 Reorder the terms: 15 + -100 + 8x + x2 = 0 Combine like terms: 15 + -100 = -85 -85 + 8x + x2 = 0 Solving -85 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 8x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 8x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 8x + x2 = 0 + 85 8x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 8x + x2 = 85 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 = 85 + 16 Reorder the terms: 16 + 8x + x2 = 85 + 16 Combine like terms: 85 + 16 = 101 16 + 8x + x2 = 101 Factor a perfect square on the left side: (x + 4)(x + 4) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + 4) equal to 10.049875621 and -10.049875621.Subproblem 1
x + 4 = 10.049875621 Simplifying x + 4 = 10.049875621 Reorder the terms: 4 + x = 10.049875621 Solving 4 + x = 10.049875621 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 = 10.049875621 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.049875621 + -4 x = 10.049875621 + -4 Combine like terms: 10.049875621 + -4 = 6.049875621 x = 6.049875621 Simplifying x = 6.049875621Subproblem 2
x + 4 = -10.049875621 Simplifying x + 4 = -10.049875621 Reorder the terms: 4 + x = -10.049875621 Solving 4 + x = -10.049875621 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 = -10.049875621 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.049875621 + -4 x = -10.049875621 + -4 Combine like terms: -10.049875621 + -4 = -14.049875621 x = -14.049875621 Simplifying x = -14.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.049875621, -14.049875621}
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