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Simplifying x2 + -17x + 21 = 0 Reorder the terms: 21 + -17x + x2 = 0 Solving 21 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -17x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -17x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -17x + x2 = 0 + -21 -17x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -17x + x2 = -21 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -21 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -21 + 72.25 Combine like terms: -21 + 72.25 = 51.25 72.25 + -17x + x2 = 51.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -8.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -8.5 = 7.158910532 Simplifying x + -8.5 = 7.158910532 Reorder the terms: -8.5 + x = 7.158910532 Solving -8.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 7.158910532 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.158910532 + 8.5 x = 7.158910532 + 8.5 Combine like terms: 7.158910532 + 8.5 = 15.658910532 x = 15.658910532 Simplifying x = 15.658910532Subproblem 2
x + -8.5 = -7.158910532 Simplifying x + -8.5 = -7.158910532 Reorder the terms: -8.5 + x = -7.158910532 Solving -8.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -7.158910532 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.158910532 + 8.5 x = -7.158910532 + 8.5 Combine like terms: -7.158910532 + 8.5 = 1.341089468 x = 1.341089468 Simplifying x = 1.341089468Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.658910532, 1.341089468}
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