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Simplifying 8x2 + -5x + -2 = 0 Reorder the terms: -2 + -5x + 8x2 = 0 Solving -2 + -5x + 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'. -0.25 + -0.625x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.625x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.625x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.625x + x2 = 0 + 0.25 -0.625x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.625x + x2 = 0.25 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 0.25 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 0.25 + 0.09765625 Combine like terms: 0.25 + 0.09765625 = 0.34765625 0.09765625 + -0.625x + x2 = 0.34765625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 0.34765625 Calculate the square root of the right side: 0.589623821 Break this problem into two subproblems by setting (x + -0.3125) equal to 0.589623821 and -0.589623821.Subproblem 1
x + -0.3125 = 0.589623821 Simplifying x + -0.3125 = 0.589623821 Reorder the terms: -0.3125 + x = 0.589623821 Solving -0.3125 + x = 0.589623821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 0.589623821 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.589623821 + 0.3125 x = 0.589623821 + 0.3125 Combine like terms: 0.589623821 + 0.3125 = 0.902123821 x = 0.902123821 Simplifying x = 0.902123821Subproblem 2
x + -0.3125 = -0.589623821 Simplifying x + -0.3125 = -0.589623821 Reorder the terms: -0.3125 + x = -0.589623821 Solving -0.3125 + x = -0.589623821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -0.589623821 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.589623821 + 0.3125 x = -0.589623821 + 0.3125 Combine like terms: -0.589623821 + 0.3125 = -0.277123821 x = -0.277123821 Simplifying x = -0.277123821Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.902123821, -0.277123821}
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