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Simplifying 0 = x2 + 4x + -496 Reorder the terms: 0 = -496 + 4x + x2 Solving 0 = -496 + 4x + x2 Solving for variable 'x'. Combine like terms: 0 + 496 = 496 496 + -4x + -1x2 = -496 + 4x + x2 + 496 + -4x + -1x2 Reorder the terms: 496 + -4x + -1x2 = -496 + 496 + 4x + -4x + x2 + -1x2 Combine like terms: -496 + 496 = 0 496 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 496 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 496 + -4x + -1x2 = 0 + x2 + -1x2 496 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 496 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -496 + 4x + x2 = 0 Move the constant term to the right: Add '496' to each side of the equation. -496 + 4x + 496 + x2 = 0 + 496 Reorder the terms: -496 + 496 + 4x + x2 = 0 + 496 Combine like terms: -496 + 496 = 0 0 + 4x + x2 = 0 + 496 4x + x2 = 0 + 496 Combine like terms: 0 + 496 = 496 4x + x2 = 496 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 496 + 4 Reorder the terms: 4 + 4x + x2 = 496 + 4 Combine like terms: 496 + 4 = 500 4 + 4x + x2 = 500 Factor a perfect square on the left side: (x + 2)(x + 2) = 500 Calculate the square root of the right side: 22.360679775 Break this problem into two subproblems by setting (x + 2) equal to 22.360679775 and -22.360679775.Subproblem 1
x + 2 = 22.360679775 Simplifying x + 2 = 22.360679775 Reorder the terms: 2 + x = 22.360679775 Solving 2 + x = 22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 22.360679775 + -2 Combine like terms: 2 + -2 = 0 0 + x = 22.360679775 + -2 x = 22.360679775 + -2 Combine like terms: 22.360679775 + -2 = 20.360679775 x = 20.360679775 Simplifying x = 20.360679775Subproblem 2
x + 2 = -22.360679775 Simplifying x + 2 = -22.360679775 Reorder the terms: 2 + x = -22.360679775 Solving 2 + x = -22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -22.360679775 + -2 Combine like terms: 2 + -2 = 0 0 + x = -22.360679775 + -2 x = -22.360679775 + -2 Combine like terms: -22.360679775 + -2 = -24.360679775 x = -24.360679775 Simplifying x = -24.360679775Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.360679775, -24.360679775}
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