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Simplifying (x + 8)(x + 6) = 32 Reorder the terms: (8 + x)(x + 6) = 32 Reorder the terms: (8 + x)(6 + x) = 32 Multiply (8 + x) * (6 + x) (8(6 + x) + x(6 + x)) = 32 ((6 * 8 + x * 8) + x(6 + x)) = 32 ((48 + 8x) + x(6 + x)) = 32 (48 + 8x + (6 * x + x * x)) = 32 (48 + 8x + (6x + x2)) = 32 Combine like terms: 8x + 6x = 14x (48 + 14x + x2) = 32 Solving 48 + 14x + x2 = 32 Solving for variable 'x'. Reorder the terms: 48 + -32 + 14x + x2 = 32 + -32 Combine like terms: 48 + -32 = 16 16 + 14x + x2 = 32 + -32 Combine like terms: 32 + -32 = 0 16 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 14x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 14x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 14x + x2 = 0 + -16 14x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 14x + x2 = -16 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -16 + 49 Reorder the terms: 49 + 14x + x2 = -16 + 49 Combine like terms: -16 + 49 = 33 49 + 14x + x2 = 33 Factor a perfect square on the left side: (x + 7)(x + 7) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 7) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 7 = 5.744562647 Simplifying x + 7 = 5.744562647 Reorder the terms: 7 + x = 5.744562647 Solving 7 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 5.744562647 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.744562647 + -7 x = 5.744562647 + -7 Combine like terms: 5.744562647 + -7 = -1.255437353 x = -1.255437353 Simplifying x = -1.255437353Subproblem 2
x + 7 = -5.744562647 Simplifying x + 7 = -5.744562647 Reorder the terms: 7 + x = -5.744562647 Solving 7 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -5.744562647 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.744562647 + -7 x = -5.744562647 + -7 Combine like terms: -5.744562647 + -7 = -12.744562647 x = -12.744562647 Simplifying x = -12.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.255437353, -12.744562647}
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