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Simplifying 16x2 + -37x + 5 = 0 Reorder the terms: 5 + -37x + 16x2 = 0 Solving 5 + -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'. 0.3125 + -2.3125x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -2.3125x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -2.3125x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -2.3125x + x2 = 0 + -0.3125 -2.3125x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -2.3125x + x2 = -0.3125 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 = -0.3125 + 1.336914063 Reorder the terms: 1.336914063 + -2.3125x + x2 = -0.3125 + 1.336914063 Combine like terms: -0.3125 + 1.336914063 = 1.024414063 1.336914063 + -2.3125x + x2 = 1.024414063 Factor a perfect square on the left side: (x + -1.15625)(x + -1.15625) = 1.024414063 Calculate the square root of the right side: 1.012133422 Break this problem into two subproblems by setting (x + -1.15625) equal to 1.012133422 and -1.012133422.Subproblem 1
x + -1.15625 = 1.012133422 Simplifying x + -1.15625 = 1.012133422 Reorder the terms: -1.15625 + x = 1.012133422 Solving -1.15625 + x = 1.012133422 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 = 1.012133422 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + x = 1.012133422 + 1.15625 x = 1.012133422 + 1.15625 Combine like terms: 1.012133422 + 1.15625 = 2.168383422 x = 2.168383422 Simplifying x = 2.168383422Subproblem 2
x + -1.15625 = -1.012133422 Simplifying x + -1.15625 = -1.012133422 Reorder the terms: -1.15625 + x = -1.012133422 Solving -1.15625 + x = -1.012133422 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 = -1.012133422 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + x = -1.012133422 + 1.15625 x = -1.012133422 + 1.15625 Combine like terms: -1.012133422 + 1.15625 = 0.144116578 x = 0.144116578 Simplifying x = 0.144116578Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.168383422, 0.144116578}
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