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Simplifying 4 = x2 + 8x + -20 Reorder the terms: 4 = -20 + 8x + x2 Solving 4 = -20 + 8x + x2 Solving for variable 'x'. Combine like terms: 4 + 20 = 24 24 + -8x + -1x2 = -20 + 8x + x2 + 20 + -8x + -1x2 Reorder the terms: 24 + -8x + -1x2 = -20 + 20 + 8x + -8x + x2 + -1x2 Combine like terms: -20 + 20 = 0 24 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 24 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 24 + -8x + -1x2 = 0 + x2 + -1x2 24 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 8x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 8x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 8x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 8x + x2 = 0 + 24 8x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 8x + x2 = 24 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 = 24 + 16 Reorder the terms: 16 + 8x + x2 = 24 + 16 Combine like terms: 24 + 16 = 40 16 + 8x + x2 = 40 Factor a perfect square on the left side: (x + 4)(x + 4) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 4) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 4 = 6.32455532 Simplifying x + 4 = 6.32455532 Reorder the terms: 4 + x = 6.32455532 Solving 4 + x = 6.32455532 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 = 6.32455532 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.32455532 + -4 x = 6.32455532 + -4 Combine like terms: 6.32455532 + -4 = 2.32455532 x = 2.32455532 Simplifying x = 2.32455532Subproblem 2
x + 4 = -6.32455532 Simplifying x + 4 = -6.32455532 Reorder the terms: 4 + x = -6.32455532 Solving 4 + x = -6.32455532 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 = -6.32455532 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.32455532 + -4 x = -6.32455532 + -4 Combine like terms: -6.32455532 + -4 = -10.32455532 x = -10.32455532 Simplifying x = -10.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.32455532, -10.32455532}
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