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Simplifying x2 + 34x + -45 = 6 Reorder the terms: -45 + 34x + x2 = 6 Solving -45 + 34x + x2 = 6 Solving for variable 'x'. Reorder the terms: -45 + -6 + 34x + x2 = 6 + -6 Combine like terms: -45 + -6 = -51 -51 + 34x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -51 + 34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 34x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 34x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 34x + x2 = 0 + 51 34x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 34x + x2 = 51 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 = 51 + 289 Reorder the terms: 289 + 34x + x2 = 51 + 289 Combine like terms: 51 + 289 = 340 289 + 34x + x2 = 340 Factor a perfect square on the left side: (x + 17)(x + 17) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (x + 17) equal to 18.439088915 and -18.439088915.Subproblem 1
x + 17 = 18.439088915 Simplifying x + 17 = 18.439088915 Reorder the terms: 17 + x = 18.439088915 Solving 17 + x = 18.439088915 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 = 18.439088915 + -17 Combine like terms: 17 + -17 = 0 0 + x = 18.439088915 + -17 x = 18.439088915 + -17 Combine like terms: 18.439088915 + -17 = 1.439088915 x = 1.439088915 Simplifying x = 1.439088915Subproblem 2
x + 17 = -18.439088915 Simplifying x + 17 = -18.439088915 Reorder the terms: 17 + x = -18.439088915 Solving 17 + x = -18.439088915 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 = -18.439088915 + -17 Combine like terms: 17 + -17 = 0 0 + x = -18.439088915 + -17 x = -18.439088915 + -17 Combine like terms: -18.439088915 + -17 = -35.439088915 x = -35.439088915 Simplifying x = -35.439088915Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.439088915, -35.439088915}
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