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Simplifying x + x2 = 11.25 Solving x + x2 = 11.25 Solving for variable 'x'. Reorder the terms: -11.25 + x + x2 = 11.25 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 -11.25 + x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + x + 11.25 + x2 = 0.00 + 11.25 Reorder the terms: -11.25 + 11.25 + x + x2 = 0.00 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x + x2 = 0.00 + 11.25 x + x2 = 0.00 + 11.25 Combine like terms: 0.00 + 11.25 = 11.25 x + x2 = 11.25 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 = 11.25 + 0.25 Reorder the terms: 0.25 + x + x2 = 11.25 + 0.25 Combine like terms: 11.25 + 0.25 = 11.5 0.25 + x + x2 = 11.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + 0.5) equal to 3.391164992 and -3.391164992.Subproblem 1
x + 0.5 = 3.391164992 Simplifying x + 0.5 = 3.391164992 Reorder the terms: 0.5 + x = 3.391164992 Solving 0.5 + x = 3.391164992 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 = 3.391164992 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.391164992 + -0.5 x = 3.391164992 + -0.5 Combine like terms: 3.391164992 + -0.5 = 2.891164992 x = 2.891164992 Simplifying x = 2.891164992Subproblem 2
x + 0.5 = -3.391164992 Simplifying x + 0.5 = -3.391164992 Reorder the terms: 0.5 + x = -3.391164992 Solving 0.5 + x = -3.391164992 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 = -3.391164992 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.391164992 + -0.5 x = -3.391164992 + -0.5 Combine like terms: -3.391164992 + -0.5 = -3.891164992 x = -3.891164992 Simplifying x = -3.891164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.891164992, -3.891164992}
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