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Simplifying x2 + -34x + 144.5 = 0 Reorder the terms: 144.5 + -34x + x2 = 0 Solving 144.5 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-144.5' to each side of the equation. 144.5 + -34x + -144.5 + x2 = 0 + -144.5 Reorder the terms: 144.5 + -144.5 + -34x + x2 = 0 + -144.5 Combine like terms: 144.5 + -144.5 = 0.0 0.0 + -34x + x2 = 0 + -144.5 -34x + x2 = 0 + -144.5 Combine like terms: 0 + -144.5 = -144.5 -34x + x2 = -144.5 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 = -144.5 + 289 Reorder the terms: 289 + -34x + x2 = -144.5 + 289 Combine like terms: -144.5 + 289 = 144.5 289 + -34x + x2 = 144.5 Factor a perfect square on the left side: (x + -17)(x + -17) = 144.5 Calculate the square root of the right side: 12.02081528 Break this problem into two subproblems by setting (x + -17) equal to 12.02081528 and -12.02081528.Subproblem 1
x + -17 = 12.02081528 Simplifying x + -17 = 12.02081528 Reorder the terms: -17 + x = 12.02081528 Solving -17 + x = 12.02081528 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 = 12.02081528 + 17 Combine like terms: -17 + 17 = 0 0 + x = 12.02081528 + 17 x = 12.02081528 + 17 Combine like terms: 12.02081528 + 17 = 29.02081528 x = 29.02081528 Simplifying x = 29.02081528Subproblem 2
x + -17 = -12.02081528 Simplifying x + -17 = -12.02081528 Reorder the terms: -17 + x = -12.02081528 Solving -17 + x = -12.02081528 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 = -12.02081528 + 17 Combine like terms: -17 + 17 = 0 0 + x = -12.02081528 + 17 x = -12.02081528 + 17 Combine like terms: -12.02081528 + 17 = 4.97918472 x = 4.97918472 Simplifying x = 4.97918472Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.02081528, 4.97918472}
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