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Simplifying 8x2 + -23x + -6 = 0 Reorder the terms: -6 + -23x + 8x2 = 0 Solving -6 + -23x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + -2.875x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2.875x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2.875x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2.875x + x2 = 0 + 0.75 -2.875x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2.875x + x2 = 0.75 The x term is -2.875x. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875x + 2.06640625 + x2 = 0.75 + 2.06640625 Reorder the terms: 2.06640625 + -2.875x + x2 = 0.75 + 2.06640625 Combine like terms: 0.75 + 2.06640625 = 2.81640625 2.06640625 + -2.875x + x2 = 2.81640625 Factor a perfect square on the left side: (x + -1.4375)(x + -1.4375) = 2.81640625 Calculate the square root of the right side: 1.678215198 Break this problem into two subproblems by setting (x + -1.4375) equal to 1.678215198 and -1.678215198.Subproblem 1
x + -1.4375 = 1.678215198 Simplifying x + -1.4375 = 1.678215198 Reorder the terms: -1.4375 + x = 1.678215198 Solving -1.4375 + x = 1.678215198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + x = 1.678215198 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = 1.678215198 + 1.4375 x = 1.678215198 + 1.4375 Combine like terms: 1.678215198 + 1.4375 = 3.115715198 x = 3.115715198 Simplifying x = 3.115715198Subproblem 2
x + -1.4375 = -1.678215198 Simplifying x + -1.4375 = -1.678215198 Reorder the terms: -1.4375 + x = -1.678215198 Solving -1.4375 + x = -1.678215198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + x = -1.678215198 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = -1.678215198 + 1.4375 x = -1.678215198 + 1.4375 Combine like terms: -1.678215198 + 1.4375 = -0.240715198 x = -0.240715198 Simplifying x = -0.240715198Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.115715198, -0.240715198}
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