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Simplifying x2 + 2x = 401.29 Reorder the terms: 2x + x2 = 401.29 Solving 2x + x2 = 401.29 Solving for variable 'x'. Reorder the terms: -401.29 + 2x + x2 = 401.29 + -401.29 Combine like terms: 401.29 + -401.29 = 0.00 -401.29 + 2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '401.29' to each side of the equation. -401.29 + 2x + 401.29 + x2 = 0.00 + 401.29 Reorder the terms: -401.29 + 401.29 + 2x + x2 = 0.00 + 401.29 Combine like terms: -401.29 + 401.29 = 0.00 0.00 + 2x + x2 = 0.00 + 401.29 2x + x2 = 0.00 + 401.29 Combine like terms: 0.00 + 401.29 = 401.29 2x + x2 = 401.29 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 401.29 + 1 Reorder the terms: 1 + 2x + x2 = 401.29 + 1 Combine like terms: 401.29 + 1 = 402.29 1 + 2x + x2 = 402.29 Factor a perfect square on the left side: (x + 1)(x + 1) = 402.29 Calculate the square root of the right side: 20.057168295 Break this problem into two subproblems by setting (x + 1) equal to 20.057168295 and -20.057168295.Subproblem 1
x + 1 = 20.057168295 Simplifying x + 1 = 20.057168295 Reorder the terms: 1 + x = 20.057168295 Solving 1 + x = 20.057168295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 20.057168295 + -1 Combine like terms: 1 + -1 = 0 0 + x = 20.057168295 + -1 x = 20.057168295 + -1 Combine like terms: 20.057168295 + -1 = 19.057168295 x = 19.057168295 Simplifying x = 19.057168295Subproblem 2
x + 1 = -20.057168295 Simplifying x + 1 = -20.057168295 Reorder the terms: 1 + x = -20.057168295 Solving 1 + x = -20.057168295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -20.057168295 + -1 Combine like terms: 1 + -1 = 0 0 + x = -20.057168295 + -1 x = -20.057168295 + -1 Combine like terms: -20.057168295 + -1 = -21.057168295 x = -21.057168295 Simplifying x = -21.057168295Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.057168295, -21.057168295}
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