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Simplifying 8x2 + 8x + -223 = 0 Reorder the terms: -223 + 8x + 8x2 = 0 Solving -223 + 8x + 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'. -27.875 + x + x2 = 0 Move the constant term to the right: Add '27.875' to each side of the equation. -27.875 + x + 27.875 + x2 = 0 + 27.875 Reorder the terms: -27.875 + 27.875 + x + x2 = 0 + 27.875 Combine like terms: -27.875 + 27.875 = 0.000 0.000 + x + x2 = 0 + 27.875 x + x2 = 0 + 27.875 Combine like terms: 0 + 27.875 = 27.875 x + x2 = 27.875 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 27.875 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 27.875 + 0.25 Combine like terms: 27.875 + 0.25 = 28.125 1.25 + x2 = 28.125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 28.125 Calculate the square root of the right side: 5.303300859 Break this problem into two subproblems by setting (x + 0.5) equal to 5.303300859 and -5.303300859.Subproblem 1
x + 0.5 = 5.303300859 Simplifying x + 0.5 = 5.303300859 Reorder the terms: 0.5 + x = 5.303300859 Solving 0.5 + x = 5.303300859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.303300859 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.303300859 + -0.5 x = 5.303300859 + -0.5 Combine like terms: 5.303300859 + -0.5 = 4.803300859 x = 4.803300859 Simplifying x = 4.803300859Subproblem 2
x + 0.5 = -5.303300859 Simplifying x + 0.5 = -5.303300859 Reorder the terms: 0.5 + x = -5.303300859 Solving 0.5 + x = -5.303300859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.303300859 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.303300859 + -0.5 x = -5.303300859 + -0.5 Combine like terms: -5.303300859 + -0.5 = -5.803300859 x = -5.803300859 Simplifying x = -5.803300859Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.803300859, -5.803300859}
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