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Simplifying x2 + 34x + 11 = 0 Reorder the terms: 11 + 34x + x2 = 0 Solving 11 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 34x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 34x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 34x + x2 = 0 + -11 34x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 34x + x2 = -11 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 = -11 + 289 Reorder the terms: 289 + 34x + x2 = -11 + 289 Combine like terms: -11 + 289 = 278 289 + 34x + x2 = 278 Factor a perfect square on the left side: (x + 17)(x + 17) = 278 Calculate the square root of the right side: 16.673332001 Break this problem into two subproblems by setting (x + 17) equal to 16.673332001 and -16.673332001.Subproblem 1
x + 17 = 16.673332001 Simplifying x + 17 = 16.673332001 Reorder the terms: 17 + x = 16.673332001 Solving 17 + x = 16.673332001 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 = 16.673332001 + -17 Combine like terms: 17 + -17 = 0 0 + x = 16.673332001 + -17 x = 16.673332001 + -17 Combine like terms: 16.673332001 + -17 = -0.326667999 x = -0.326667999 Simplifying x = -0.326667999Subproblem 2
x + 17 = -16.673332001 Simplifying x + 17 = -16.673332001 Reorder the terms: 17 + x = -16.673332001 Solving 17 + x = -16.673332001 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 = -16.673332001 + -17 Combine like terms: 17 + -17 = 0 0 + x = -16.673332001 + -17 x = -16.673332001 + -17 Combine like terms: -16.673332001 + -17 = -33.673332001 x = -33.673332001 Simplifying x = -33.673332001Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.326667999, -33.673332001}
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