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Simplifying x2 + 8x + -460 = 0 Reorder the terms: -460 + 8x + x2 = 0 Solving -460 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '460' to each side of the equation. -460 + 8x + 460 + x2 = 0 + 460 Reorder the terms: -460 + 460 + 8x + x2 = 0 + 460 Combine like terms: -460 + 460 = 0 0 + 8x + x2 = 0 + 460 8x + x2 = 0 + 460 Combine like terms: 0 + 460 = 460 8x + x2 = 460 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 = 460 + 16 Reorder the terms: 16 + 8x + x2 = 460 + 16 Combine like terms: 460 + 16 = 476 16 + 8x + x2 = 476 Factor a perfect square on the left side: (x + 4)(x + 4) = 476 Calculate the square root of the right side: 21.817424229 Break this problem into two subproblems by setting (x + 4) equal to 21.817424229 and -21.817424229.Subproblem 1
x + 4 = 21.817424229 Simplifying x + 4 = 21.817424229 Reorder the terms: 4 + x = 21.817424229 Solving 4 + x = 21.817424229 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 = 21.817424229 + -4 Combine like terms: 4 + -4 = 0 0 + x = 21.817424229 + -4 x = 21.817424229 + -4 Combine like terms: 21.817424229 + -4 = 17.817424229 x = 17.817424229 Simplifying x = 17.817424229Subproblem 2
x + 4 = -21.817424229 Simplifying x + 4 = -21.817424229 Reorder the terms: 4 + x = -21.817424229 Solving 4 + x = -21.817424229 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 = -21.817424229 + -4 Combine like terms: 4 + -4 = 0 0 + x = -21.817424229 + -4 x = -21.817424229 + -4 Combine like terms: -21.817424229 + -4 = -25.817424229 x = -25.817424229 Simplifying x = -25.817424229Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.817424229, -25.817424229}
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