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Simplifying x2 + -17x + 62 = 0 Reorder the terms: 62 + -17x + x2 = 0 Solving 62 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-62' to each side of the equation. 62 + -17x + -62 + x2 = 0 + -62 Reorder the terms: 62 + -62 + -17x + x2 = 0 + -62 Combine like terms: 62 + -62 = 0 0 + -17x + x2 = 0 + -62 -17x + x2 = 0 + -62 Combine like terms: 0 + -62 = -62 -17x + x2 = -62 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 = -62 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -62 + 72.25 Combine like terms: -62 + 72.25 = 10.25 72.25 + -17x + x2 = 10.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -8.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -8.5 = 3.201562119 Simplifying x + -8.5 = 3.201562119 Reorder the terms: -8.5 + x = 3.201562119 Solving -8.5 + x = 3.201562119 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 = 3.201562119 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 3.201562119 + 8.5 x = 3.201562119 + 8.5 Combine like terms: 3.201562119 + 8.5 = 11.701562119 x = 11.701562119 Simplifying x = 11.701562119Subproblem 2
x + -8.5 = -3.201562119 Simplifying x + -8.5 = -3.201562119 Reorder the terms: -8.5 + x = -3.201562119 Solving -8.5 + x = -3.201562119 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 = -3.201562119 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -3.201562119 + 8.5 x = -3.201562119 + 8.5 Combine like terms: -3.201562119 + 8.5 = 5.298437881 x = 5.298437881 Simplifying x = 5.298437881Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.701562119, 5.298437881}
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