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Simplifying 0 = x2 + 10x + -512 Reorder the terms: 0 = -512 + 10x + x2 Solving 0 = -512 + 10x + x2 Solving for variable 'x'. Combine like terms: 0 + 512 = 512 512 + -10x + -1x2 = -512 + 10x + x2 + 512 + -10x + -1x2 Reorder the terms: 512 + -10x + -1x2 = -512 + 512 + 10x + -10x + x2 + -1x2 Combine like terms: -512 + 512 = 0 512 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 512 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 512 + -10x + -1x2 = 0 + x2 + -1x2 512 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 512 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -512 + 10x + x2 = 0 Move the constant term to the right: Add '512' to each side of the equation. -512 + 10x + 512 + x2 = 0 + 512 Reorder the terms: -512 + 512 + 10x + x2 = 0 + 512 Combine like terms: -512 + 512 = 0 0 + 10x + x2 = 0 + 512 10x + x2 = 0 + 512 Combine like terms: 0 + 512 = 512 10x + x2 = 512 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 512 + 25 Reorder the terms: 25 + 10x + x2 = 512 + 25 Combine like terms: 512 + 25 = 537 25 + 10x + x2 = 537 Factor a perfect square on the left side: (x + 5)(x + 5) = 537 Calculate the square root of the right side: 23.173260453 Break this problem into two subproblems by setting (x + 5) equal to 23.173260453 and -23.173260453.Subproblem 1
x + 5 = 23.173260453 Simplifying x + 5 = 23.173260453 Reorder the terms: 5 + x = 23.173260453 Solving 5 + x = 23.173260453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 23.173260453 + -5 Combine like terms: 5 + -5 = 0 0 + x = 23.173260453 + -5 x = 23.173260453 + -5 Combine like terms: 23.173260453 + -5 = 18.173260453 x = 18.173260453 Simplifying x = 18.173260453Subproblem 2
x + 5 = -23.173260453 Simplifying x + 5 = -23.173260453 Reorder the terms: 5 + x = -23.173260453 Solving 5 + x = -23.173260453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -23.173260453 + -5 Combine like terms: 5 + -5 = 0 0 + x = -23.173260453 + -5 x = -23.173260453 + -5 Combine like terms: -23.173260453 + -5 = -28.173260453 x = -28.173260453 Simplifying x = -28.173260453Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.173260453, -28.173260453}
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