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Simplifying -16x2 + 56x + 1 = 0 Reorder the terms: 1 + 56x + -16x2 = 0 Solving 1 + 56x + -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'. -0.0625 + -3.5x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -3.5x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -3.5x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -3.5x + x2 = 0 + 0.0625 -3.5x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -3.5x + x2 = 0.0625 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 0.0625 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 0.0625 + 3.0625 Combine like terms: 0.0625 + 3.0625 = 3.125 3.0625 + -3.5x + x2 = 3.125 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (x + -1.75) equal to 1.767766953 and -1.767766953.Subproblem 1
x + -1.75 = 1.767766953 Simplifying x + -1.75 = 1.767766953 Reorder the terms: -1.75 + x = 1.767766953 Solving -1.75 + x = 1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.767766953 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.767766953 + 1.75 x = 1.767766953 + 1.75 Combine like terms: 1.767766953 + 1.75 = 3.517766953 x = 3.517766953 Simplifying x = 3.517766953Subproblem 2
x + -1.75 = -1.767766953 Simplifying x + -1.75 = -1.767766953 Reorder the terms: -1.75 + x = -1.767766953 Solving -1.75 + x = -1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.767766953 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.767766953 + 1.75 x = -1.767766953 + 1.75 Combine like terms: -1.767766953 + 1.75 = -0.017766953 x = -0.017766953 Simplifying x = -0.017766953Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.517766953, -0.017766953}
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