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Simplifying 32x2 + -96x + 35 = 0 Reorder the terms: 35 + -96x + 32x2 = 0 Solving 35 + -96x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 1.09375 + -3x + x2 = 0 Move the constant term to the right: Add '-1.09375' to each side of the equation. 1.09375 + -3x + -1.09375 + x2 = 0 + -1.09375 Reorder the terms: 1.09375 + -1.09375 + -3x + x2 = 0 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + -3x + x2 = 0 + -1.09375 -3x + x2 = 0 + -1.09375 Combine like terms: 0 + -1.09375 = -1.09375 -3x + x2 = -1.09375 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.09375 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.09375 + 2.25 Combine like terms: -1.09375 + 2.25 = 1.15625 2.25 + -3x + x2 = 1.15625 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.15625 Calculate the square root of the right side: 1.075290658 Break this problem into two subproblems by setting (x + -1.5) equal to 1.075290658 and -1.075290658.Subproblem 1
x + -1.5 = 1.075290658 Simplifying x + -1.5 = 1.075290658 Reorder the terms: -1.5 + x = 1.075290658 Solving -1.5 + x = 1.075290658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.075290658 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.075290658 + 1.5 x = 1.075290658 + 1.5 Combine like terms: 1.075290658 + 1.5 = 2.575290658 x = 2.575290658 Simplifying x = 2.575290658Subproblem 2
x + -1.5 = -1.075290658 Simplifying x + -1.5 = -1.075290658 Reorder the terms: -1.5 + x = -1.075290658 Solving -1.5 + x = -1.075290658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.075290658 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.075290658 + 1.5 x = -1.075290658 + 1.5 Combine like terms: -1.075290658 + 1.5 = 0.424709342 x = 0.424709342 Simplifying x = 0.424709342Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.575290658, 0.424709342}
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