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Simplifying x2 + 2x = 144 Reorder the terms: 2x + x2 = 144 Solving 2x + x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 2x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 2x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 2x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 2x + x2 = 0 + 144 2x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 2x + x2 = 144 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 = 144 + 1 Reorder the terms: 1 + 2x + x2 = 144 + 1 Combine like terms: 144 + 1 = 145 1 + 2x + x2 = 145 Factor a perfect square on the left side: (x + 1)(x + 1) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + 1) equal to 12.041594579 and -12.041594579.Subproblem 1
x + 1 = 12.041594579 Simplifying x + 1 = 12.041594579 Reorder the terms: 1 + x = 12.041594579 Solving 1 + x = 12.041594579 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 = 12.041594579 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.041594579 + -1 x = 12.041594579 + -1 Combine like terms: 12.041594579 + -1 = 11.041594579 x = 11.041594579 Simplifying x = 11.041594579Subproblem 2
x + 1 = -12.041594579 Simplifying x + 1 = -12.041594579 Reorder the terms: 1 + x = -12.041594579 Solving 1 + x = -12.041594579 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 = -12.041594579 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.041594579 + -1 x = -12.041594579 + -1 Combine like terms: -12.041594579 + -1 = -13.041594579 x = -13.041594579 Simplifying x = -13.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.041594579, -13.041594579}
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