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Simplifying 16x2 + -37x + -14 = 0 Reorder the terms: -14 + -37x + 16x2 = 0 Solving -14 + -37x + 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'. -0.875 + -2.3125x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -2.3125x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -2.3125x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -2.3125x + x2 = 0 + 0.875 -2.3125x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -2.3125x + x2 = 0.875 The x term is -2.3125x. Take half its coefficient (-1.15625). Square it (1.336914063) and add it to both sides. Add '1.336914063' to each side of the equation. -2.3125x + 1.336914063 + x2 = 0.875 + 1.336914063 Reorder the terms: 1.336914063 + -2.3125x + x2 = 0.875 + 1.336914063 Combine like terms: 0.875 + 1.336914063 = 2.211914063 1.336914063 + -2.3125x + x2 = 2.211914063 Factor a perfect square on the left side: (x + -1.15625)(x + -1.15625) = 2.211914063 Calculate the square root of the right side: 1.487250504 Break this problem into two subproblems by setting (x + -1.15625) equal to 1.487250504 and -1.487250504.Subproblem 1
x + -1.15625 = 1.487250504 Simplifying x + -1.15625 = 1.487250504 Reorder the terms: -1.15625 + x = 1.487250504 Solving -1.15625 + x = 1.487250504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + x = 1.487250504 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + x = 1.487250504 + 1.15625 x = 1.487250504 + 1.15625 Combine like terms: 1.487250504 + 1.15625 = 2.643500504 x = 2.643500504 Simplifying x = 2.643500504Subproblem 2
x + -1.15625 = -1.487250504 Simplifying x + -1.15625 = -1.487250504 Reorder the terms: -1.15625 + x = -1.487250504 Solving -1.15625 + x = -1.487250504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + x = -1.487250504 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + x = -1.487250504 + 1.15625 x = -1.487250504 + 1.15625 Combine like terms: -1.487250504 + 1.15625 = -0.331000504 x = -0.331000504 Simplifying x = -0.331000504Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.643500504, -0.331000504}
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