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Simplifying 16x2 + -112x + 135 = 0 Reorder the terms: 135 + -112x + 16x2 = 0 Solving 135 + -112x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 8.4375 + -7x + x2 = 0 Move the constant term to the right: Add '-8.4375' to each side of the equation. 8.4375 + -7x + -8.4375 + x2 = 0 + -8.4375 Reorder the terms: 8.4375 + -8.4375 + -7x + x2 = 0 + -8.4375 Combine like terms: 8.4375 + -8.4375 = 0.0000 0.0000 + -7x + x2 = 0 + -8.4375 -7x + x2 = 0 + -8.4375 Combine like terms: 0 + -8.4375 = -8.4375 -7x + x2 = -8.4375 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -8.4375 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -8.4375 + 12.25 Combine like terms: -8.4375 + 12.25 = 3.8125 12.25 + -7x + x2 = 3.8125 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (x + -3.5) equal to 1.952562419 and -1.952562419.Subproblem 1
x + -3.5 = 1.952562419 Simplifying x + -3.5 = 1.952562419 Reorder the terms: -3.5 + x = 1.952562419 Solving -3.5 + x = 1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.952562419 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.952562419 + 3.5 x = 1.952562419 + 3.5 Combine like terms: 1.952562419 + 3.5 = 5.452562419 x = 5.452562419 Simplifying x = 5.452562419Subproblem 2
x + -3.5 = -1.952562419 Simplifying x + -3.5 = -1.952562419 Reorder the terms: -3.5 + x = -1.952562419 Solving -3.5 + x = -1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.952562419 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.952562419 + 3.5 x = -1.952562419 + 3.5 Combine like terms: -1.952562419 + 3.5 = 1.547437581 x = 1.547437581 Simplifying x = 1.547437581Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.452562419, 1.547437581}
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