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Simplifying x2 + -21x + 45 = 0 Reorder the terms: 45 + -21x + x2 = 0 Solving 45 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -21x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -21x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -21x + x2 = 0 + -45 -21x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -21x + x2 = -45 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -45 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -45 + 110.25 Combine like terms: -45 + 110.25 = 65.25 110.25 + -21x + x2 = 65.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + -10.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + -10.5 = 8.077747211 Simplifying x + -10.5 = 8.077747211 Reorder the terms: -10.5 + x = 8.077747211 Solving -10.5 + x = 8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 8.077747211 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 8.077747211 + 10.5 x = 8.077747211 + 10.5 Combine like terms: 8.077747211 + 10.5 = 18.577747211 x = 18.577747211 Simplifying x = 18.577747211Subproblem 2
x + -10.5 = -8.077747211 Simplifying x + -10.5 = -8.077747211 Reorder the terms: -10.5 + x = -8.077747211 Solving -10.5 + x = -8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -8.077747211 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -8.077747211 + 10.5 x = -8.077747211 + 10.5 Combine like terms: -8.077747211 + 10.5 = 2.422252789 x = 2.422252789 Simplifying x = 2.422252789Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.577747211, 2.422252789}
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