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Simplifying -16x2 + 35x = 0.5 Reorder the terms: 35x + -16x2 = 0.5 Solving 35x + -16x2 = 0.5 Solving for variable 'x'. Reorder the terms: -0.5 + 35x + -16x2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + 35x + -16x2 = 0.0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.03125 + -2.1875x + x2 = 0.0 Move the constant term to the right: Add '-0.03125' to each side of the equation. 0.03125 + -2.1875x + -0.03125 + x2 = 0.0 + -0.03125 Reorder the terms: 0.03125 + -0.03125 + -2.1875x + x2 = 0.0 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + -2.1875x + x2 = 0.0 + -0.03125 -2.1875x + x2 = 0.0 + -0.03125 Combine like terms: 0.0 + -0.03125 = -0.03125 -2.1875x + x2 = -0.03125 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 = -0.03125 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875x + x2 = -0.03125 + 1.196289063 Combine like terms: -0.03125 + 1.196289063 = 1.165039063 1.196289063 + -2.1875x + x2 = 1.165039063 Factor a perfect square on the left side: (x + -1.09375)(x + -1.09375) = 1.165039063 Calculate the square root of the right side: 1.079369753 Break this problem into two subproblems by setting (x + -1.09375) equal to 1.079369753 and -1.079369753.Subproblem 1
x + -1.09375 = 1.079369753 Simplifying x + -1.09375 = 1.079369753 Reorder the terms: -1.09375 + x = 1.079369753 Solving -1.09375 + x = 1.079369753 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 = 1.079369753 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 1.079369753 + 1.09375 x = 1.079369753 + 1.09375 Combine like terms: 1.079369753 + 1.09375 = 2.173119753 x = 2.173119753 Simplifying x = 2.173119753Subproblem 2
x + -1.09375 = -1.079369753 Simplifying x + -1.09375 = -1.079369753 Reorder the terms: -1.09375 + x = -1.079369753 Solving -1.09375 + x = -1.079369753 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 = -1.079369753 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -1.079369753 + 1.09375 x = -1.079369753 + 1.09375 Combine like terms: -1.079369753 + 1.09375 = 0.014380247 x = 0.014380247 Simplifying x = 0.014380247Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.173119753, 0.014380247}
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