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Simplifying x2 + -34x + 51 = 0 Reorder the terms: 51 + -34x + x2 = 0 Solving 51 + -34x + x2 = 0 Solving for variable 'x'. 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 = 238 289 + -34x + x2 = 238 Factor a perfect square on the left side: (x + -17)(x + -17) = 238 Calculate the square root of the right side: 15.427248621 Break this problem into two subproblems by setting (x + -17) equal to 15.427248621 and -15.427248621.Subproblem 1
x + -17 = 15.427248621 Simplifying x + -17 = 15.427248621 Reorder the terms: -17 + x = 15.427248621 Solving -17 + x = 15.427248621 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 = 15.427248621 + 17 Combine like terms: -17 + 17 = 0 0 + x = 15.427248621 + 17 x = 15.427248621 + 17 Combine like terms: 15.427248621 + 17 = 32.427248621 x = 32.427248621 Simplifying x = 32.427248621Subproblem 2
x + -17 = -15.427248621 Simplifying x + -17 = -15.427248621 Reorder the terms: -17 + x = -15.427248621 Solving -17 + x = -15.427248621 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 = -15.427248621 + 17 Combine like terms: -17 + 17 = 0 0 + x = -15.427248621 + 17 x = -15.427248621 + 17 Combine like terms: -15.427248621 + 17 = 1.572751379 x = 1.572751379 Simplifying x = 1.572751379Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.427248621, 1.572751379}
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