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Simplifying x(x + 1) = 1050 Reorder the terms: x(1 + x) = 1050 (1 * x + x * x) = 1050 (1x + x2) = 1050 Solving 1x + x2 = 1050 Solving for variable 'x'. Reorder the terms: -1050 + 1x + x2 = 1050 + -1050 Combine like terms: 1050 + -1050 = 0 -1050 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1050' to each side of the equation. -1050 + 1x + 1050 + x2 = 0 + 1050 Reorder the terms: -1050 + 1050 + 1x + x2 = 0 + 1050 Combine like terms: -1050 + 1050 = 0 0 + 1x + x2 = 0 + 1050 1x + x2 = 0 + 1050 Combine like terms: 0 + 1050 = 1050 1x + x2 = 1050 The x term is 1x. 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 = 1050 + 0.25 Reorder the terms: 0.25 + x + x2 = 1050 + 0.25 Combine like terms: 1050 + 0.25 = 1050.25 0.25 + x + x2 = 1050.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1050.25 Calculate the square root of the right side: 32.407560846 Break this problem into two subproblems by setting (x + 0.5) equal to 32.407560846 and -32.407560846.Subproblem 1
x + 0.5 = 32.407560846 Simplifying x + 0.5 = 32.407560846 Reorder the terms: 0.5 + x = 32.407560846 Solving 0.5 + x = 32.407560846 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 = 32.407560846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 32.407560846 + -0.5 x = 32.407560846 + -0.5 Combine like terms: 32.407560846 + -0.5 = 31.907560846 x = 31.907560846 Simplifying x = 31.907560846Subproblem 2
x + 0.5 = -32.407560846 Simplifying x + 0.5 = -32.407560846 Reorder the terms: 0.5 + x = -32.407560846 Solving 0.5 + x = -32.407560846 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 = -32.407560846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -32.407560846 + -0.5 x = -32.407560846 + -0.5 Combine like terms: -32.407560846 + -0.5 = -32.907560846 x = -32.907560846 Simplifying x = -32.907560846Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.907560846, -32.907560846}
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