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Simplifying 10 = -16x2 + 27x + 6 Reorder the terms: 10 = 6 + 27x + -16x2 Solving 10 = 6 + 27x + -16x2 Solving for variable 'x'. Combine like terms: 10 + -6 = 4 4 + -27x + 16x2 = 6 + 27x + -16x2 + -6 + -27x + 16x2 Reorder the terms: 4 + -27x + 16x2 = 6 + -6 + 27x + -27x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 4 + -27x + 16x2 = 0 + 27x + -27x + -16x2 + 16x2 4 + -27x + 16x2 = 27x + -27x + -16x2 + 16x2 Combine like terms: 27x + -27x = 0 4 + -27x + 16x2 = 0 + -16x2 + 16x2 4 + -27x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 4 + -27x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + -1.6875x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.6875x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.6875x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.6875x + x2 = 0 + -0.25 -1.6875x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.6875x + x2 = -0.25 The x term is -1.6875x. Take half its coefficient (-0.84375). Square it (0.7119140625) and add it to both sides. Add '0.7119140625' to each side of the equation. -1.6875x + 0.7119140625 + x2 = -0.25 + 0.7119140625 Reorder the terms: 0.7119140625 + -1.6875x + x2 = -0.25 + 0.7119140625 Combine like terms: -0.25 + 0.7119140625 = 0.4619140625 0.7119140625 + -1.6875x + x2 = 0.4619140625 Factor a perfect square on the left side: (x + -0.84375)(x + -0.84375) = 0.4619140625 Calculate the square root of the right side: 0.679642599 Break this problem into two subproblems by setting (x + -0.84375) equal to 0.679642599 and -0.679642599.Subproblem 1
x + -0.84375 = 0.679642599 Simplifying x + -0.84375 = 0.679642599 Reorder the terms: -0.84375 + x = 0.679642599 Solving -0.84375 + x = 0.679642599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.84375' to each side of the equation. -0.84375 + 0.84375 + x = 0.679642599 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + x = 0.679642599 + 0.84375 x = 0.679642599 + 0.84375 Combine like terms: 0.679642599 + 0.84375 = 1.523392599 x = 1.523392599 Simplifying x = 1.523392599Subproblem 2
x + -0.84375 = -0.679642599 Simplifying x + -0.84375 = -0.679642599 Reorder the terms: -0.84375 + x = -0.679642599 Solving -0.84375 + x = -0.679642599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.84375' to each side of the equation. -0.84375 + 0.84375 + x = -0.679642599 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + x = -0.679642599 + 0.84375 x = -0.679642599 + 0.84375 Combine like terms: -0.679642599 + 0.84375 = 0.164107401 x = 0.164107401 Simplifying x = 0.164107401Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.523392599, 0.164107401}
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