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Simplifying 16x2 + -9 = 2x + 6 Reorder the terms: -9 + 16x2 = 2x + 6 Reorder the terms: -9 + 16x2 = 6 + 2x Solving -9 + 16x2 = 6 + 2x Solving for variable 'x'. Reorder the terms: -9 + -6 + -2x + 16x2 = 6 + 2x + -6 + -2x Combine like terms: -9 + -6 = -15 -15 + -2x + 16x2 = 6 + 2x + -6 + -2x Reorder the terms: -15 + -2x + 16x2 = 6 + -6 + 2x + -2x Combine like terms: 6 + -6 = 0 -15 + -2x + 16x2 = 0 + 2x + -2x -15 + -2x + 16x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -15 + -2x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -0.125x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -0.125x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -0.125x + x2 = 0 + 0.9375 -0.125x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -0.125x + x2 = 0.9375 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 0.9375 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.9375 + 0.00390625 Combine like terms: 0.9375 + 0.00390625 = 0.94140625 0.00390625 + -0.125x + x2 = 0.94140625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.970260919 and -0.970260919.Subproblem 1
x + -0.0625 = 0.970260919 Simplifying x + -0.0625 = 0.970260919 Reorder the terms: -0.0625 + x = 0.970260919 Solving -0.0625 + x = 0.970260919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.970260919 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.970260919 + 0.0625 x = 0.970260919 + 0.0625 Combine like terms: 0.970260919 + 0.0625 = 1.032760919 x = 1.032760919 Simplifying x = 1.032760919Subproblem 2
x + -0.0625 = -0.970260919 Simplifying x + -0.0625 = -0.970260919 Reorder the terms: -0.0625 + x = -0.970260919 Solving -0.0625 + x = -0.970260919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.970260919 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.970260919 + 0.0625 x = -0.970260919 + 0.0625 Combine like terms: -0.970260919 + 0.0625 = -0.907760919 x = -0.907760919 Simplifying x = -0.907760919Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.032760919, -0.907760919}
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