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Simplifying 0 = 16x2 + -5x + -14 Reorder the terms: 0 = -14 + -5x + 16x2 Solving 0 = -14 + -5x + 16x2 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + 5x + -16x2 = -14 + -5x + 16x2 + 14 + 5x + -16x2 Reorder the terms: 14 + 5x + -16x2 = -14 + 14 + -5x + 5x + 16x2 + -16x2 Combine like terms: -14 + 14 = 0 14 + 5x + -16x2 = 0 + -5x + 5x + 16x2 + -16x2 14 + 5x + -16x2 = -5x + 5x + 16x2 + -16x2 Combine like terms: -5x + 5x = 0 14 + 5x + -16x2 = 0 + 16x2 + -16x2 14 + 5x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 14 + 5x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.875 + -0.3125x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.3125x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.3125x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.3125x + x2 = 0 + 0.875 -0.3125x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.3125x + x2 = 0.875 The x term is -0.3125x. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125x + 0.0244140625 + x2 = 0.875 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125x + x2 = 0.875 + 0.0244140625 Combine like terms: 0.875 + 0.0244140625 = 0.8994140625 0.0244140625 + -0.3125x + x2 = 0.8994140625 Factor a perfect square on the left side: (x + -0.15625)(x + -0.15625) = 0.8994140625 Calculate the square root of the right side: 0.948374432 Break this problem into two subproblems by setting (x + -0.15625) equal to 0.948374432 and -0.948374432.Subproblem 1
x + -0.15625 = 0.948374432 Simplifying x + -0.15625 = 0.948374432 Reorder the terms: -0.15625 + x = 0.948374432 Solving -0.15625 + x = 0.948374432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = 0.948374432 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = 0.948374432 + 0.15625 x = 0.948374432 + 0.15625 Combine like terms: 0.948374432 + 0.15625 = 1.104624432 x = 1.104624432 Simplifying x = 1.104624432Subproblem 2
x + -0.15625 = -0.948374432 Simplifying x + -0.15625 = -0.948374432 Reorder the terms: -0.15625 + x = -0.948374432 Solving -0.15625 + x = -0.948374432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = -0.948374432 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = -0.948374432 + 0.15625 x = -0.948374432 + 0.15625 Combine like terms: -0.948374432 + 0.15625 = -0.792124432 x = -0.792124432 Simplifying x = -0.792124432Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.104624432, -0.792124432}
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