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Simplifying x2 + 8x + -974 = 0 Reorder the terms: -974 + 8x + x2 = 0 Solving -974 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '974' to each side of the equation. -974 + 8x + 974 + x2 = 0 + 974 Reorder the terms: -974 + 974 + 8x + x2 = 0 + 974 Combine like terms: -974 + 974 = 0 0 + 8x + x2 = 0 + 974 8x + x2 = 0 + 974 Combine like terms: 0 + 974 = 974 8x + x2 = 974 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 = 974 + 16 Reorder the terms: 16 + 8x + x2 = 974 + 16 Combine like terms: 974 + 16 = 990 16 + 8x + x2 = 990 Factor a perfect square on the left side: (x + 4)(x + 4) = 990 Calculate the square root of the right side: 31.464265445 Break this problem into two subproblems by setting (x + 4) equal to 31.464265445 and -31.464265445.Subproblem 1
x + 4 = 31.464265445 Simplifying x + 4 = 31.464265445 Reorder the terms: 4 + x = 31.464265445 Solving 4 + x = 31.464265445 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 = 31.464265445 + -4 Combine like terms: 4 + -4 = 0 0 + x = 31.464265445 + -4 x = 31.464265445 + -4 Combine like terms: 31.464265445 + -4 = 27.464265445 x = 27.464265445 Simplifying x = 27.464265445Subproblem 2
x + 4 = -31.464265445 Simplifying x + 4 = -31.464265445 Reorder the terms: 4 + x = -31.464265445 Solving 4 + x = -31.464265445 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 = -31.464265445 + -4 Combine like terms: 4 + -4 = 0 0 + x = -31.464265445 + -4 x = -31.464265445 + -4 Combine like terms: -31.464265445 + -4 = -35.464265445 x = -35.464265445 Simplifying x = -35.464265445Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.464265445, -35.464265445}
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