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Simplifying x2 + -34x + 154 = 0 Reorder the terms: 154 + -34x + x2 = 0 Solving 154 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-154' to each side of the equation. 154 + -34x + -154 + x2 = 0 + -154 Reorder the terms: 154 + -154 + -34x + x2 = 0 + -154 Combine like terms: 154 + -154 = 0 0 + -34x + x2 = 0 + -154 -34x + x2 = 0 + -154 Combine like terms: 0 + -154 = -154 -34x + x2 = -154 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 = -154 + 289 Reorder the terms: 289 + -34x + x2 = -154 + 289 Combine like terms: -154 + 289 = 135 289 + -34x + x2 = 135 Factor a perfect square on the left side: (x + -17)(x + -17) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (x + -17) equal to 11.618950039 and -11.618950039.Subproblem 1
x + -17 = 11.618950039 Simplifying x + -17 = 11.618950039 Reorder the terms: -17 + x = 11.618950039 Solving -17 + x = 11.618950039 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 = 11.618950039 + 17 Combine like terms: -17 + 17 = 0 0 + x = 11.618950039 + 17 x = 11.618950039 + 17 Combine like terms: 11.618950039 + 17 = 28.618950039 x = 28.618950039 Simplifying x = 28.618950039Subproblem 2
x + -17 = -11.618950039 Simplifying x + -17 = -11.618950039 Reorder the terms: -17 + x = -11.618950039 Solving -17 + x = -11.618950039 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 = -11.618950039 + 17 Combine like terms: -17 + 17 = 0 0 + x = -11.618950039 + 17 x = -11.618950039 + 17 Combine like terms: -11.618950039 + 17 = 5.381049961 x = 5.381049961 Simplifying x = 5.381049961Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.618950039, 5.381049961}
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