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Simplifying x2 + x + -8.67 = 0 Reorder the terms: -8.67 + x + x2 = 0 Solving -8.67 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8.67' to each side of the equation. -8.67 + x + 8.67 + x2 = 0 + 8.67 Reorder the terms: -8.67 + 8.67 + x + x2 = 0 + 8.67 Combine like terms: -8.67 + 8.67 = 0.00 0.00 + x + x2 = 0 + 8.67 x + x2 = 0 + 8.67 Combine like terms: 0 + 8.67 = 8.67 x + x2 = 8.67 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. x + 0.25 + x2 = 8.67 + 0.25 Reorder the terms: 0.25 + x + x2 = 8.67 + 0.25 Combine like terms: 8.67 + 0.25 = 8.92 0.25 + x + x2 = 8.92 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8.92 Calculate the square root of the right side: 2.986636905 Break this problem into two subproblems by setting (x + 0.5) equal to 2.986636905 and -2.986636905.Subproblem 1
x + 0.5 = 2.986636905 Simplifying x + 0.5 = 2.986636905 Reorder the terms: 0.5 + x = 2.986636905 Solving 0.5 + x = 2.986636905 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 = 2.986636905 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.986636905 + -0.5 x = 2.986636905 + -0.5 Combine like terms: 2.986636905 + -0.5 = 2.486636905 x = 2.486636905 Simplifying x = 2.486636905Subproblem 2
x + 0.5 = -2.986636905 Simplifying x + 0.5 = -2.986636905 Reorder the terms: 0.5 + x = -2.986636905 Solving 0.5 + x = -2.986636905 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 = -2.986636905 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.986636905 + -0.5 x = -2.986636905 + -0.5 Combine like terms: -2.986636905 + -0.5 = -3.486636905 x = -3.486636905 Simplifying x = -3.486636905Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.486636905, -3.486636905}
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