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Simplifying 8x2 + 4x + -85 = 0 Reorder the terms: -85 + 4x + 8x2 = 0 Solving -85 + 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'. -10.625 + 0.5x + x2 = 0 Move the constant term to the right: Add '10.625' to each side of the equation. -10.625 + 0.5x + 10.625 + x2 = 0 + 10.625 Reorder the terms: -10.625 + 10.625 + 0.5x + x2 = 0 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + 0.5x + x2 = 0 + 10.625 0.5x + x2 = 0 + 10.625 Combine like terms: 0 + 10.625 = 10.625 0.5x + x2 = 10.625 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 = 10.625 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 10.625 + 0.0625 Combine like terms: 10.625 + 0.0625 = 10.6875 0.0625 + 0.5x + x2 = 10.6875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 10.6875 Calculate the square root of the right side: 3.269174208 Break this problem into two subproblems by setting (x + 0.25) equal to 3.269174208 and -3.269174208.Subproblem 1
x + 0.25 = 3.269174208 Simplifying x + 0.25 = 3.269174208 Reorder the terms: 0.25 + x = 3.269174208 Solving 0.25 + x = 3.269174208 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 = 3.269174208 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.269174208 + -0.25 x = 3.269174208 + -0.25 Combine like terms: 3.269174208 + -0.25 = 3.019174208 x = 3.019174208 Simplifying x = 3.019174208Subproblem 2
x + 0.25 = -3.269174208 Simplifying x + 0.25 = -3.269174208 Reorder the terms: 0.25 + x = -3.269174208 Solving 0.25 + x = -3.269174208 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 = -3.269174208 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.269174208 + -0.25 x = -3.269174208 + -0.25 Combine like terms: -3.269174208 + -0.25 = -3.519174208 x = -3.519174208 Simplifying x = -3.519174208Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.019174208, -3.519174208}
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