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Simplifying 8x2 + -20x + -21 = 0 Reorder the terms: -21 + -20x + 8x2 = 0 Solving -21 + -20x + 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'. -2.625 + -2.5x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -2.5x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -2.5x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -2.5x + x2 = 0 + 2.625 -2.5x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -2.5x + x2 = 2.625 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 2.625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 2.625 + 1.5625 Combine like terms: 2.625 + 1.5625 = 4.1875 1.5625 + -2.5x + x2 = 4.1875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 4.1875 Calculate the square root of the right side: 2.046338193 Break this problem into two subproblems by setting (x + -1.25) equal to 2.046338193 and -2.046338193.Subproblem 1
x + -1.25 = 2.046338193 Simplifying x + -1.25 = 2.046338193 Reorder the terms: -1.25 + x = 2.046338193 Solving -1.25 + x = 2.046338193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.046338193 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.046338193 + 1.25 x = 2.046338193 + 1.25 Combine like terms: 2.046338193 + 1.25 = 3.296338193 x = 3.296338193 Simplifying x = 3.296338193Subproblem 2
x + -1.25 = -2.046338193 Simplifying x + -1.25 = -2.046338193 Reorder the terms: -1.25 + x = -2.046338193 Solving -1.25 + x = -2.046338193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.046338193 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.046338193 + 1.25 x = -2.046338193 + 1.25 Combine like terms: -2.046338193 + 1.25 = -0.796338193 x = -0.796338193 Simplifying x = -0.796338193Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.296338193, -0.796338193}
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