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Simplifying -1x2 + 8x + 23 = 0 Reorder the terms: 23 + 8x + -1x2 = 0 Solving 23 + 8x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + -8x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + -8x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -8x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -8x + x2 = 0 + 23 -8x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -8x + x2 = 23 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 = 23 + 16 Reorder the terms: 16 + -8x + x2 = 23 + 16 Combine like terms: 23 + 16 = 39 16 + -8x + x2 = 39 Factor a perfect square on the left side: (x + -4)(x + -4) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -4) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -4 = 6.244997998 Simplifying x + -4 = 6.244997998 Reorder the terms: -4 + x = 6.244997998 Solving -4 + x = 6.244997998 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 = 6.244997998 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.244997998 + 4 x = 6.244997998 + 4 Combine like terms: 6.244997998 + 4 = 10.244997998 x = 10.244997998 Simplifying x = 10.244997998Subproblem 2
x + -4 = -6.244997998 Simplifying x + -4 = -6.244997998 Reorder the terms: -4 + x = -6.244997998 Solving -4 + x = -6.244997998 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 = -6.244997998 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.244997998 + 4 x = -6.244997998 + 4 Combine like terms: -6.244997998 + 4 = -2.244997998 x = -2.244997998 Simplifying x = -2.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.244997998, -2.244997998}
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