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Simplifying 16x2 + -35x + -3 = 0 Reorder the terms: -3 + -35x + 16x2 = 0 Solving -3 + -35x + 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'. -0.1875 + -2.1875x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -2.1875x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -2.1875x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -2.1875x + x2 = 0 + 0.1875 -2.1875x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -2.1875x + x2 = 0.1875 The x term is -2.1875x. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875x + 1.196289063 + x2 = 0.1875 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875x + x2 = 0.1875 + 1.196289063 Combine like terms: 0.1875 + 1.196289063 = 1.383789063 1.196289063 + -2.1875x + x2 = 1.383789063 Factor a perfect square on the left side: (x + -1.09375)(x + -1.09375) = 1.383789063 Calculate the square root of the right side: 1.176345639 Break this problem into two subproblems by setting (x + -1.09375) equal to 1.176345639 and -1.176345639.Subproblem 1
x + -1.09375 = 1.176345639 Simplifying x + -1.09375 = 1.176345639 Reorder the terms: -1.09375 + x = 1.176345639 Solving -1.09375 + x = 1.176345639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = 1.176345639 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 1.176345639 + 1.09375 x = 1.176345639 + 1.09375 Combine like terms: 1.176345639 + 1.09375 = 2.270095639 x = 2.270095639 Simplifying x = 2.270095639Subproblem 2
x + -1.09375 = -1.176345639 Simplifying x + -1.09375 = -1.176345639 Reorder the terms: -1.09375 + x = -1.176345639 Solving -1.09375 + x = -1.176345639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = -1.176345639 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -1.176345639 + 1.09375 x = -1.176345639 + 1.09375 Combine like terms: -1.176345639 + 1.09375 = -0.082595639 x = -0.082595639 Simplifying x = -0.082595639Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.270095639, -0.082595639}
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