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Simplifying x2 + 8x + -184 = 0 Reorder the terms: -184 + 8x + x2 = 0 Solving -184 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '184' to each side of the equation. -184 + 8x + 184 + x2 = 0 + 184 Reorder the terms: -184 + 184 + 8x + x2 = 0 + 184 Combine like terms: -184 + 184 = 0 0 + 8x + x2 = 0 + 184 8x + x2 = 0 + 184 Combine like terms: 0 + 184 = 184 8x + x2 = 184 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 = 184 + 16 Reorder the terms: 16 + 8x + x2 = 184 + 16 Combine like terms: 184 + 16 = 200 16 + 8x + x2 = 200 Factor a perfect square on the left side: (x + 4)(x + 4) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + 4) equal to 14.142135624 and -14.142135624.Subproblem 1
x + 4 = 14.142135624 Simplifying x + 4 = 14.142135624 Reorder the terms: 4 + x = 14.142135624 Solving 4 + x = 14.142135624 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 = 14.142135624 + -4 Combine like terms: 4 + -4 = 0 0 + x = 14.142135624 + -4 x = 14.142135624 + -4 Combine like terms: 14.142135624 + -4 = 10.142135624 x = 10.142135624 Simplifying x = 10.142135624Subproblem 2
x + 4 = -14.142135624 Simplifying x + 4 = -14.142135624 Reorder the terms: 4 + x = -14.142135624 Solving 4 + x = -14.142135624 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 = -14.142135624 + -4 Combine like terms: 4 + -4 = 0 0 + x = -14.142135624 + -4 x = -14.142135624 + -4 Combine like terms: -14.142135624 + -4 = -18.142135624 x = -18.142135624 Simplifying x = -18.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.142135624, -18.142135624}
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