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Simplifying x2 + 8x + -15 = 14 Reorder the terms: -15 + 8x + x2 = 14 Solving -15 + 8x + x2 = 14 Solving for variable 'x'. Reorder the terms: -15 + -14 + 8x + x2 = 14 + -14 Combine like terms: -15 + -14 = -29 -29 + 8x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -29 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 8x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 8x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 8x + x2 = 0 + 29 8x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 8x + x2 = 29 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 = 29 + 16 Reorder the terms: 16 + 8x + x2 = 29 + 16 Combine like terms: 29 + 16 = 45 16 + 8x + x2 = 45 Factor a perfect square on the left side: (x + 4)(x + 4) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 4) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 4 = 6.708203933 Simplifying x + 4 = 6.708203933 Reorder the terms: 4 + x = 6.708203933 Solving 4 + x = 6.708203933 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 = 6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.708203933 + -4 x = 6.708203933 + -4 Combine like terms: 6.708203933 + -4 = 2.708203933 x = 2.708203933 Simplifying x = 2.708203933Subproblem 2
x + 4 = -6.708203933 Simplifying x + 4 = -6.708203933 Reorder the terms: 4 + x = -6.708203933 Solving 4 + x = -6.708203933 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 = -6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.708203933 + -4 x = -6.708203933 + -4 Combine like terms: -6.708203933 + -4 = -10.708203933 x = -10.708203933 Simplifying x = -10.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.708203933, -10.708203933}
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