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Simplifying x2 + x = 3150 Reorder the terms: x + x2 = 3150 Solving x + x2 = 3150 Solving for variable 'x'. Reorder the terms: -3150 + x + x2 = 3150 + -3150 Combine like terms: 3150 + -3150 = 0 -3150 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3150' to each side of the equation. -3150 + x + 3150 + x2 = 0 + 3150 Reorder the terms: -3150 + 3150 + x + x2 = 0 + 3150 Combine like terms: -3150 + 3150 = 0 0 + x + x2 = 0 + 3150 x + x2 = 0 + 3150 Combine like terms: 0 + 3150 = 3150 x + x2 = 3150 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 = 3150 + 0.25 Reorder the terms: 0.25 + x + x2 = 3150 + 0.25 Combine like terms: 3150 + 0.25 = 3150.25 0.25 + x + x2 = 3150.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3150.25 Calculate the square root of the right side: 56.127087934 Break this problem into two subproblems by setting (x + 0.5) equal to 56.127087934 and -56.127087934.Subproblem 1
x + 0.5 = 56.127087934 Simplifying x + 0.5 = 56.127087934 Reorder the terms: 0.5 + x = 56.127087934 Solving 0.5 + x = 56.127087934 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 = 56.127087934 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 56.127087934 + -0.5 x = 56.127087934 + -0.5 Combine like terms: 56.127087934 + -0.5 = 55.627087934 x = 55.627087934 Simplifying x = 55.627087934Subproblem 2
x + 0.5 = -56.127087934 Simplifying x + 0.5 = -56.127087934 Reorder the terms: 0.5 + x = -56.127087934 Solving 0.5 + x = -56.127087934 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 = -56.127087934 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -56.127087934 + -0.5 x = -56.127087934 + -0.5 Combine like terms: -56.127087934 + -0.5 = -56.627087934 x = -56.627087934 Simplifying x = -56.627087934Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.627087934, -56.627087934}
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