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Simplifying x2 + 34x + 94 = 0 Reorder the terms: 94 + 34x + x2 = 0 Solving 94 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-94' to each side of the equation. 94 + 34x + -94 + x2 = 0 + -94 Reorder the terms: 94 + -94 + 34x + x2 = 0 + -94 Combine like terms: 94 + -94 = 0 0 + 34x + x2 = 0 + -94 34x + x2 = 0 + -94 Combine like terms: 0 + -94 = -94 34x + x2 = -94 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 = -94 + 289 Reorder the terms: 289 + 34x + x2 = -94 + 289 Combine like terms: -94 + 289 = 195 289 + 34x + x2 = 195 Factor a perfect square on the left side: (x + 17)(x + 17) = 195 Calculate the square root of the right side: 13.964240044 Break this problem into two subproblems by setting (x + 17) equal to 13.964240044 and -13.964240044.Subproblem 1
x + 17 = 13.964240044 Simplifying x + 17 = 13.964240044 Reorder the terms: 17 + x = 13.964240044 Solving 17 + x = 13.964240044 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 = 13.964240044 + -17 Combine like terms: 17 + -17 = 0 0 + x = 13.964240044 + -17 x = 13.964240044 + -17 Combine like terms: 13.964240044 + -17 = -3.035759956 x = -3.035759956 Simplifying x = -3.035759956Subproblem 2
x + 17 = -13.964240044 Simplifying x + 17 = -13.964240044 Reorder the terms: 17 + x = -13.964240044 Solving 17 + x = -13.964240044 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 = -13.964240044 + -17 Combine like terms: 17 + -17 = 0 0 + x = -13.964240044 + -17 x = -13.964240044 + -17 Combine like terms: -13.964240044 + -17 = -30.964240044 x = -30.964240044 Simplifying x = -30.964240044Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.035759956, -30.964240044}
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