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Simplifying x2 + 34x + 144 = 0 Reorder the terms: 144 + 34x + x2 = 0 Solving 144 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + 34x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + 34x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + 34x + x2 = 0 + -144 34x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 34x + x2 = -144 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = -144 + 289 Reorder the terms: 289 + 34x + x2 = -144 + 289 Combine like terms: -144 + 289 = 145 289 + 34x + x2 = 145 Factor a perfect square on the left side: (x + 17)(x + 17) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + 17) equal to 12.041594579 and -12.041594579.Subproblem 1
x + 17 = 12.041594579 Simplifying x + 17 = 12.041594579 Reorder the terms: 17 + x = 12.041594579 Solving 17 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 12.041594579 + -17 Combine like terms: 17 + -17 = 0 0 + x = 12.041594579 + -17 x = 12.041594579 + -17 Combine like terms: 12.041594579 + -17 = -4.958405421 x = -4.958405421 Simplifying x = -4.958405421Subproblem 2
x + 17 = -12.041594579 Simplifying x + 17 = -12.041594579 Reorder the terms: 17 + x = -12.041594579 Solving 17 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -12.041594579 + -17 Combine like terms: 17 + -17 = 0 0 + x = -12.041594579 + -17 x = -12.041594579 + -17 Combine like terms: -12.041594579 + -17 = -29.041594579 x = -29.041594579 Simplifying x = -29.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.958405421, -29.041594579}
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