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Simplifying 8x2 + -4x + -63 = 0 Reorder the terms: -63 + -4x + 8x2 = 0 Solving -63 + -4x + 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'. -7.875 + -0.5x + x2 = 0 Move the constant term to the right: Add '7.875' to each side of the equation. -7.875 + -0.5x + 7.875 + x2 = 0 + 7.875 Reorder the terms: -7.875 + 7.875 + -0.5x + x2 = 0 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + -0.5x + x2 = 0 + 7.875 -0.5x + x2 = 0 + 7.875 Combine like terms: 0 + 7.875 = 7.875 -0.5x + x2 = 7.875 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 7.875 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 7.875 + 0.0625 Combine like terms: 7.875 + 0.0625 = 7.9375 0.0625 + -0.5x + x2 = 7.9375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 7.9375 Calculate the square root of the right side: 2.817356917 Break this problem into two subproblems by setting (x + -0.25) equal to 2.817356917 and -2.817356917.Subproblem 1
x + -0.25 = 2.817356917 Simplifying x + -0.25 = 2.817356917 Reorder the terms: -0.25 + x = 2.817356917 Solving -0.25 + x = 2.817356917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.817356917 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.817356917 + 0.25 x = 2.817356917 + 0.25 Combine like terms: 2.817356917 + 0.25 = 3.067356917 x = 3.067356917 Simplifying x = 3.067356917Subproblem 2
x + -0.25 = -2.817356917 Simplifying x + -0.25 = -2.817356917 Reorder the terms: -0.25 + x = -2.817356917 Solving -0.25 + x = -2.817356917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.817356917 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.817356917 + 0.25 x = -2.817356917 + 0.25 Combine like terms: -2.817356917 + 0.25 = -2.567356917 x = -2.567356917 Simplifying x = -2.567356917Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.067356917, -2.567356917}
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