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Simplifying 0 = x2 + 32x + -345 Reorder the terms: 0 = -345 + 32x + x2 Solving 0 = -345 + 32x + x2 Solving for variable 'x'. Combine like terms: 0 + 345 = 345 345 + -32x + -1x2 = -345 + 32x + x2 + 345 + -32x + -1x2 Reorder the terms: 345 + -32x + -1x2 = -345 + 345 + 32x + -32x + x2 + -1x2 Combine like terms: -345 + 345 = 0 345 + -32x + -1x2 = 0 + 32x + -32x + x2 + -1x2 345 + -32x + -1x2 = 32x + -32x + x2 + -1x2 Combine like terms: 32x + -32x = 0 345 + -32x + -1x2 = 0 + x2 + -1x2 345 + -32x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 345 + -32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -345 + 32x + x2 = 0 Move the constant term to the right: Add '345' to each side of the equation. -345 + 32x + 345 + x2 = 0 + 345 Reorder the terms: -345 + 345 + 32x + x2 = 0 + 345 Combine like terms: -345 + 345 = 0 0 + 32x + x2 = 0 + 345 32x + x2 = 0 + 345 Combine like terms: 0 + 345 = 345 32x + x2 = 345 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 = 345 + 256 Reorder the terms: 256 + 32x + x2 = 345 + 256 Combine like terms: 345 + 256 = 601 256 + 32x + x2 = 601 Factor a perfect square on the left side: (x + 16)(x + 16) = 601 Calculate the square root of the right side: 24.515301344 Break this problem into two subproblems by setting (x + 16) equal to 24.515301344 and -24.515301344.Subproblem 1
x + 16 = 24.515301344 Simplifying x + 16 = 24.515301344 Reorder the terms: 16 + x = 24.515301344 Solving 16 + x = 24.515301344 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 = 24.515301344 + -16 Combine like terms: 16 + -16 = 0 0 + x = 24.515301344 + -16 x = 24.515301344 + -16 Combine like terms: 24.515301344 + -16 = 8.515301344 x = 8.515301344 Simplifying x = 8.515301344Subproblem 2
x + 16 = -24.515301344 Simplifying x + 16 = -24.515301344 Reorder the terms: 16 + x = -24.515301344 Solving 16 + x = -24.515301344 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 = -24.515301344 + -16 Combine like terms: 16 + -16 = 0 0 + x = -24.515301344 + -16 x = -24.515301344 + -16 Combine like terms: -24.515301344 + -16 = -40.515301344 x = -40.515301344 Simplifying x = -40.515301344Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.515301344, -40.515301344}
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