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Simplifying x2 + 2x = 10300 Reorder the terms: 2x + x2 = 10300 Solving 2x + x2 = 10300 Solving for variable 'x'. Reorder the terms: -10300 + 2x + x2 = 10300 + -10300 Combine like terms: 10300 + -10300 = 0 -10300 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10300' to each side of the equation. -10300 + 2x + 10300 + x2 = 0 + 10300 Reorder the terms: -10300 + 10300 + 2x + x2 = 0 + 10300 Combine like terms: -10300 + 10300 = 0 0 + 2x + x2 = 0 + 10300 2x + x2 = 0 + 10300 Combine like terms: 0 + 10300 = 10300 2x + x2 = 10300 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 = 10300 + 1 Reorder the terms: 1 + 2x + x2 = 10300 + 1 Combine like terms: 10300 + 1 = 10301 1 + 2x + x2 = 10301 Factor a perfect square on the left side: (x + 1)(x + 1) = 10301 Calculate the square root of the right side: 101.493842178 Break this problem into two subproblems by setting (x + 1) equal to 101.493842178 and -101.493842178.Subproblem 1
x + 1 = 101.493842178 Simplifying x + 1 = 101.493842178 Reorder the terms: 1 + x = 101.493842178 Solving 1 + x = 101.493842178 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 = 101.493842178 + -1 Combine like terms: 1 + -1 = 0 0 + x = 101.493842178 + -1 x = 101.493842178 + -1 Combine like terms: 101.493842178 + -1 = 100.493842178 x = 100.493842178 Simplifying x = 100.493842178Subproblem 2
x + 1 = -101.493842178 Simplifying x + 1 = -101.493842178 Reorder the terms: 1 + x = -101.493842178 Solving 1 + x = -101.493842178 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 = -101.493842178 + -1 Combine like terms: 1 + -1 = 0 0 + x = -101.493842178 + -1 x = -101.493842178 + -1 Combine like terms: -101.493842178 + -1 = -102.493842178 x = -102.493842178 Simplifying x = -102.493842178Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.493842178, -102.493842178}
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