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Simplifying 0 = x2 + 32x + -744 Reorder the terms: 0 = -744 + 32x + x2 Solving 0 = -744 + 32x + x2 Solving for variable 'x'. Combine like terms: 0 + 744 = 744 744 + -32x + -1x2 = -744 + 32x + x2 + 744 + -32x + -1x2 Reorder the terms: 744 + -32x + -1x2 = -744 + 744 + 32x + -32x + x2 + -1x2 Combine like terms: -744 + 744 = 0 744 + -32x + -1x2 = 0 + 32x + -32x + x2 + -1x2 744 + -32x + -1x2 = 32x + -32x + x2 + -1x2 Combine like terms: 32x + -32x = 0 744 + -32x + -1x2 = 0 + x2 + -1x2 744 + -32x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 744 + -32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -744 + 32x + x2 = 0 Move the constant term to the right: Add '744' to each side of the equation. -744 + 32x + 744 + x2 = 0 + 744 Reorder the terms: -744 + 744 + 32x + x2 = 0 + 744 Combine like terms: -744 + 744 = 0 0 + 32x + x2 = 0 + 744 32x + x2 = 0 + 744 Combine like terms: 0 + 744 = 744 32x + x2 = 744 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 744 + 256 Reorder the terms: 256 + 32x + x2 = 744 + 256 Combine like terms: 744 + 256 = 1000 256 + 32x + x2 = 1000 Factor a perfect square on the left side: (x + 16)(x + 16) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + 16) equal to 31.622776602 and -31.622776602.Subproblem 1
x + 16 = 31.622776602 Simplifying x + 16 = 31.622776602 Reorder the terms: 16 + x = 31.622776602 Solving 16 + x = 31.622776602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 31.622776602 + -16 Combine like terms: 16 + -16 = 0 0 + x = 31.622776602 + -16 x = 31.622776602 + -16 Combine like terms: 31.622776602 + -16 = 15.622776602 x = 15.622776602 Simplifying x = 15.622776602Subproblem 2
x + 16 = -31.622776602 Simplifying x + 16 = -31.622776602 Reorder the terms: 16 + x = -31.622776602 Solving 16 + x = -31.622776602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -31.622776602 + -16 Combine like terms: 16 + -16 = 0 0 + x = -31.622776602 + -16 x = -31.622776602 + -16 Combine like terms: -31.622776602 + -16 = -47.622776602 x = -47.622776602 Simplifying x = -47.622776602Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.622776602, -47.622776602}
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