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Simplifying 16x2 + -35x + 15 = 0 Reorder the terms: 15 + -35x + 16x2 = 0 Solving 15 + -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'. 0.9375 + -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 = 0.258789063 1.196289063 + -2.1875x + x2 = 0.258789063 Factor a perfect square on the left side: (x + -1.09375)(x + -1.09375) = 0.258789063 Calculate the square root of the right side: 0.508713144 Break this problem into two subproblems by setting (x + -1.09375) equal to 0.508713144 and -0.508713144.Subproblem 1
x + -1.09375 = 0.508713144 Simplifying x + -1.09375 = 0.508713144 Reorder the terms: -1.09375 + x = 0.508713144 Solving -1.09375 + x = 0.508713144 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 = 0.508713144 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 0.508713144 + 1.09375 x = 0.508713144 + 1.09375 Combine like terms: 0.508713144 + 1.09375 = 1.602463144 x = 1.602463144 Simplifying x = 1.602463144Subproblem 2
x + -1.09375 = -0.508713144 Simplifying x + -1.09375 = -0.508713144 Reorder the terms: -1.09375 + x = -0.508713144 Solving -1.09375 + x = -0.508713144 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 = -0.508713144 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -0.508713144 + 1.09375 x = -0.508713144 + 1.09375 Combine like terms: -0.508713144 + 1.09375 = 0.585036856 x = 0.585036856 Simplifying x = 0.585036856Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.602463144, 0.585036856}
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