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Simplifying -1x2 + 30x + 32 = 0 Reorder the terms: 32 + 30x + -1x2 = 0 Solving 32 + 30x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -32 + -30x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -30x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -30x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -30x + x2 = 0 + 32 -30x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -30x + x2 = 32 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 32 + 225 Reorder the terms: 225 + -30x + x2 = 32 + 225 Combine like terms: 32 + 225 = 257 225 + -30x + x2 = 257 Factor a perfect square on the left side: (x + -15)(x + -15) = 257 Calculate the square root of the right side: 16.031219542 Break this problem into two subproblems by setting (x + -15) equal to 16.031219542 and -16.031219542.Subproblem 1
x + -15 = 16.031219542 Simplifying x + -15 = 16.031219542 Reorder the terms: -15 + x = 16.031219542 Solving -15 + x = 16.031219542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 16.031219542 + 15 Combine like terms: -15 + 15 = 0 0 + x = 16.031219542 + 15 x = 16.031219542 + 15 Combine like terms: 16.031219542 + 15 = 31.031219542 x = 31.031219542 Simplifying x = 31.031219542Subproblem 2
x + -15 = -16.031219542 Simplifying x + -15 = -16.031219542 Reorder the terms: -15 + x = -16.031219542 Solving -15 + x = -16.031219542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -16.031219542 + 15 Combine like terms: -15 + 15 = 0 0 + x = -16.031219542 + 15 x = -16.031219542 + 15 Combine like terms: -16.031219542 + 15 = -1.031219542 x = -1.031219542 Simplifying x = -1.031219542Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.031219542, -1.031219542}
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