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Simplifying x + x2 = 68 Solving x + x2 = 68 Solving for variable 'x'. Reorder the terms: -68 + x + x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + x + x2 = 0 + 68 x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 x + x2 = 68 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 = 68 + 0.25 Reorder the terms: 0.25 + x + x2 = 68 + 0.25 Combine like terms: 68 + 0.25 = 68.25 0.25 + x + x2 = 68.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 0.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + 0.5 = 8.261355821 Simplifying x + 0.5 = 8.261355821 Reorder the terms: 0.5 + x = 8.261355821 Solving 0.5 + x = 8.261355821 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 = 8.261355821 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.261355821 + -0.5 x = 8.261355821 + -0.5 Combine like terms: 8.261355821 + -0.5 = 7.761355821 x = 7.761355821 Simplifying x = 7.761355821Subproblem 2
x + 0.5 = -8.261355821 Simplifying x + 0.5 = -8.261355821 Reorder the terms: 0.5 + x = -8.261355821 Solving 0.5 + x = -8.261355821 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 = -8.261355821 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.261355821 + -0.5 x = -8.261355821 + -0.5 Combine like terms: -8.261355821 + -0.5 = -8.761355821 x = -8.761355821 Simplifying x = -8.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.761355821, -8.761355821}
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