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Simplifying 0 = -16x2 + 35x + 15 Reorder the terms: 0 = 15 + 35x + -16x2 Solving 0 = 15 + 35x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -35x + 16x2 = 15 + 35x + -16x2 + -15 + -35x + 16x2 Reorder the terms: -15 + -35x + 16x2 = 15 + -15 + 35x + -35x + -16x2 + 16x2 Combine like terms: 15 + -15 = 0 -15 + -35x + 16x2 = 0 + 35x + -35x + -16x2 + 16x2 -15 + -35x + 16x2 = 35x + -35x + -16x2 + 16x2 Combine like terms: 35x + -35x = 0 -15 + -35x + 16x2 = 0 + -16x2 + 16x2 -15 + -35x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -15 + -35x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -2.1875x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -2.1875x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -2.1875x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -2.1875x + x2 = 0 + 0.9375 -2.1875x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -2.1875x + x2 = 0.9375 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 = 0.9375 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875x + x2 = 0.9375 + 1.196289063 Combine like terms: 0.9375 + 1.196289063 = 2.133789063 1.196289063 + -2.1875x + x2 = 2.133789063 Factor a perfect square on the left side: (x + -1.09375)(x + -1.09375) = 2.133789063 Calculate the square root of the right side: 1.460749487 Break this problem into two subproblems by setting (x + -1.09375) equal to 1.460749487 and -1.460749487.Subproblem 1
x + -1.09375 = 1.460749487 Simplifying x + -1.09375 = 1.460749487 Reorder the terms: -1.09375 + x = 1.460749487 Solving -1.09375 + x = 1.460749487 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 = 1.460749487 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 1.460749487 + 1.09375 x = 1.460749487 + 1.09375 Combine like terms: 1.460749487 + 1.09375 = 2.554499487 x = 2.554499487 Simplifying x = 2.554499487Subproblem 2
x + -1.09375 = -1.460749487 Simplifying x + -1.09375 = -1.460749487 Reorder the terms: -1.09375 + x = -1.460749487 Solving -1.09375 + x = -1.460749487 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 = -1.460749487 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -1.460749487 + 1.09375 x = -1.460749487 + 1.09375 Combine like terms: -1.460749487 + 1.09375 = -0.366999487 x = -0.366999487 Simplifying x = -0.366999487Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.554499487, -0.366999487}
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