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Simplifying -16x2 + 104x + 56 = 3.25 Reorder the terms: 56 + 104x + -16x2 = 3.25 Solving 56 + 104x + -16x2 = 3.25 Solving for variable 'x'. Reorder the terms: 56 + -3.25 + 104x + -16x2 = 3.25 + -3.25 Combine like terms: 56 + -3.25 = 52.75 52.75 + 104x + -16x2 = 3.25 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 52.75 + 104x + -16x2 = 0.00 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -3.296875 + -6.5x + x2 = 0.00 Move the constant term to the right: Add '3.296875' to each side of the equation. -3.296875 + -6.5x + 3.296875 + x2 = 0.00 + 3.296875 Reorder the terms: -3.296875 + 3.296875 + -6.5x + x2 = 0.00 + 3.296875 Combine like terms: -3.296875 + 3.296875 = 0.000000 0.000000 + -6.5x + x2 = 0.00 + 3.296875 -6.5x + x2 = 0.00 + 3.296875 Combine like terms: 0.00 + 3.296875 = 3.296875 -6.5x + x2 = 3.296875 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 3.296875 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 3.296875 + 10.5625 Combine like terms: 3.296875 + 10.5625 = 13.859375 10.5625 + -6.5x + x2 = 13.859375 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 13.859375 Calculate the square root of the right side: 3.722818153 Break this problem into two subproblems by setting (x + -3.25) equal to 3.722818153 and -3.722818153.Subproblem 1
x + -3.25 = 3.722818153 Simplifying x + -3.25 = 3.722818153 Reorder the terms: -3.25 + x = 3.722818153 Solving -3.25 + x = 3.722818153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 3.722818153 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.722818153 + 3.25 x = 3.722818153 + 3.25 Combine like terms: 3.722818153 + 3.25 = 6.972818153 x = 6.972818153 Simplifying x = 6.972818153Subproblem 2
x + -3.25 = -3.722818153 Simplifying x + -3.25 = -3.722818153 Reorder the terms: -3.25 + x = -3.722818153 Solving -3.25 + x = -3.722818153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -3.722818153 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.722818153 + 3.25 x = -3.722818153 + 3.25 Combine like terms: -3.722818153 + 3.25 = -0.472818153 x = -0.472818153 Simplifying x = -0.472818153Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.972818153, -0.472818153}
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