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Simplifying x2 + 8x + -465 = 0 Reorder the terms: -465 + 8x + x2 = 0 Solving -465 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '465' to each side of the equation. -465 + 8x + 465 + x2 = 0 + 465 Reorder the terms: -465 + 465 + 8x + x2 = 0 + 465 Combine like terms: -465 + 465 = 0 0 + 8x + x2 = 0 + 465 8x + x2 = 0 + 465 Combine like terms: 0 + 465 = 465 8x + x2 = 465 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 = 465 + 16 Reorder the terms: 16 + 8x + x2 = 465 + 16 Combine like terms: 465 + 16 = 481 16 + 8x + x2 = 481 Factor a perfect square on the left side: (x + 4)(x + 4) = 481 Calculate the square root of the right side: 21.931712199 Break this problem into two subproblems by setting (x + 4) equal to 21.931712199 and -21.931712199.Subproblem 1
x + 4 = 21.931712199 Simplifying x + 4 = 21.931712199 Reorder the terms: 4 + x = 21.931712199 Solving 4 + x = 21.931712199 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 = 21.931712199 + -4 Combine like terms: 4 + -4 = 0 0 + x = 21.931712199 + -4 x = 21.931712199 + -4 Combine like terms: 21.931712199 + -4 = 17.931712199 x = 17.931712199 Simplifying x = 17.931712199Subproblem 2
x + 4 = -21.931712199 Simplifying x + 4 = -21.931712199 Reorder the terms: 4 + x = -21.931712199 Solving 4 + x = -21.931712199 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 = -21.931712199 + -4 Combine like terms: 4 + -4 = 0 0 + x = -21.931712199 + -4 x = -21.931712199 + -4 Combine like terms: -21.931712199 + -4 = -25.931712199 x = -25.931712199 Simplifying x = -25.931712199Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.931712199, -25.931712199}
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