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Simplifying x2 + 34x + -37 = 0 Reorder the terms: -37 + 34x + x2 = 0 Solving -37 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 34x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 34x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 34x + x2 = 0 + 37 34x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 34x + x2 = 37 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 = 37 + 289 Reorder the terms: 289 + 34x + x2 = 37 + 289 Combine like terms: 37 + 289 = 326 289 + 34x + x2 = 326 Factor a perfect square on the left side: (x + 17)(x + 17) = 326 Calculate the square root of the right side: 18.055470085 Break this problem into two subproblems by setting (x + 17) equal to 18.055470085 and -18.055470085.Subproblem 1
x + 17 = 18.055470085 Simplifying x + 17 = 18.055470085 Reorder the terms: 17 + x = 18.055470085 Solving 17 + x = 18.055470085 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 = 18.055470085 + -17 Combine like terms: 17 + -17 = 0 0 + x = 18.055470085 + -17 x = 18.055470085 + -17 Combine like terms: 18.055470085 + -17 = 1.055470085 x = 1.055470085 Simplifying x = 1.055470085Subproblem 2
x + 17 = -18.055470085 Simplifying x + 17 = -18.055470085 Reorder the terms: 17 + x = -18.055470085 Solving 17 + x = -18.055470085 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 = -18.055470085 + -17 Combine like terms: 17 + -17 = 0 0 + x = -18.055470085 + -17 x = -18.055470085 + -17 Combine like terms: -18.055470085 + -17 = -35.055470085 x = -35.055470085 Simplifying x = -35.055470085Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.055470085, -35.055470085}
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