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Simplifying x2 + x = 8100 Reorder the terms: x + x2 = 8100 Solving x + x2 = 8100 Solving for variable 'x'. Reorder the terms: -8100 + x + x2 = 8100 + -8100 Combine like terms: 8100 + -8100 = 0 -8100 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8100' to each side of the equation. -8100 + x + 8100 + x2 = 0 + 8100 Reorder the terms: -8100 + 8100 + x + x2 = 0 + 8100 Combine like terms: -8100 + 8100 = 0 0 + x + x2 = 0 + 8100 x + x2 = 0 + 8100 Combine like terms: 0 + 8100 = 8100 x + x2 = 8100 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 = 8100 + 0.25 Reorder the terms: 0.25 + x + x2 = 8100 + 0.25 Combine like terms: 8100 + 0.25 = 8100.25 0.25 + x + x2 = 8100.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8100.25 Calculate the square root of the right side: 90.001388878 Break this problem into two subproblems by setting (x + 0.5) equal to 90.001388878 and -90.001388878.Subproblem 1
x + 0.5 = 90.001388878 Simplifying x + 0.5 = 90.001388878 Reorder the terms: 0.5 + x = 90.001388878 Solving 0.5 + x = 90.001388878 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 = 90.001388878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 90.001388878 + -0.5 x = 90.001388878 + -0.5 Combine like terms: 90.001388878 + -0.5 = 89.501388878 x = 89.501388878 Simplifying x = 89.501388878Subproblem 2
x + 0.5 = -90.001388878 Simplifying x + 0.5 = -90.001388878 Reorder the terms: 0.5 + x = -90.001388878 Solving 0.5 + x = -90.001388878 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 = -90.001388878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -90.001388878 + -0.5 x = -90.001388878 + -0.5 Combine like terms: -90.001388878 + -0.5 = -90.501388878 x = -90.501388878 Simplifying x = -90.501388878Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.501388878, -90.501388878}
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