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Simplifying 8x2 + -11 = 6x Reorder the terms: -11 + 8x2 = 6x Solving -11 + 8x2 = 6x Solving for variable 'x'. Reorder the terms: -11 + -6x + 8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -11 + -6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + -0.75x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -0.75x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -0.75x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -0.75x + x2 = 0 + 1.375 -0.75x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -0.75x + x2 = 1.375 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 1.375 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 1.375 + 0.140625 Combine like terms: 1.375 + 0.140625 = 1.515625 0.140625 + -0.75x + x2 = 1.515625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + -0.375) equal to 1.231107225 and -1.231107225.Subproblem 1
x + -0.375 = 1.231107225 Simplifying x + -0.375 = 1.231107225 Reorder the terms: -0.375 + x = 1.231107225 Solving -0.375 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.231107225 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.231107225 + 0.375 x = 1.231107225 + 0.375 Combine like terms: 1.231107225 + 0.375 = 1.606107225 x = 1.606107225 Simplifying x = 1.606107225Subproblem 2
x + -0.375 = -1.231107225 Simplifying x + -0.375 = -1.231107225 Reorder the terms: -0.375 + x = -1.231107225 Solving -0.375 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.231107225 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.231107225 + 0.375 x = -1.231107225 + 0.375 Combine like terms: -1.231107225 + 0.375 = -0.856107225 x = -0.856107225 Simplifying x = -0.856107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.606107225, -0.856107225}
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