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Simplifying 16x2 + -215x + 96 = 0 Reorder the terms: 96 + -215x + 16x2 = 0 Solving 96 + -215x + 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'. 6 + -13.4375x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -13.4375x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -13.4375x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -13.4375x + x2 = 0 + -6 -13.4375x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -13.4375x + x2 = -6 The x term is -13.4375x. Take half its coefficient (-6.71875). Square it (45.14160156) and add it to both sides. Add '45.14160156' to each side of the equation. -13.4375x + 45.14160156 + x2 = -6 + 45.14160156 Reorder the terms: 45.14160156 + -13.4375x + x2 = -6 + 45.14160156 Combine like terms: -6 + 45.14160156 = 39.14160156 45.14160156 + -13.4375x + x2 = 39.14160156 Factor a perfect square on the left side: (x + -6.71875)(x + -6.71875) = 39.14160156 Calculate the square root of the right side: 6.256324924 Break this problem into two subproblems by setting (x + -6.71875) equal to 6.256324924 and -6.256324924.Subproblem 1
x + -6.71875 = 6.256324924 Simplifying x + -6.71875 = 6.256324924 Reorder the terms: -6.71875 + x = 6.256324924 Solving -6.71875 + x = 6.256324924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + x = 6.256324924 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + x = 6.256324924 + 6.71875 x = 6.256324924 + 6.71875 Combine like terms: 6.256324924 + 6.71875 = 12.975074924 x = 12.975074924 Simplifying x = 12.975074924Subproblem 2
x + -6.71875 = -6.256324924 Simplifying x + -6.71875 = -6.256324924 Reorder the terms: -6.71875 + x = -6.256324924 Solving -6.71875 + x = -6.256324924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + x = -6.256324924 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + x = -6.256324924 + 6.71875 x = -6.256324924 + 6.71875 Combine like terms: -6.256324924 + 6.71875 = 0.462425076 x = 0.462425076 Simplifying x = 0.462425076Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.975074924, 0.462425076}
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