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Simplifying -1x2 + -21x + 80 = 0 Reorder the terms: 80 + -21x + -1x2 = 0 Solving 80 + -21x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + 21x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 21x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 21x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 21x + x2 = 0 + 80 21x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 21x + x2 = 80 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 = 80 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 80 + 110.25 Combine like terms: 80 + 110.25 = 190.25 110.25 + 21x + x2 = 190.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + 10.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + 10.5 = 13.793114224 Simplifying x + 10.5 = 13.793114224 Reorder the terms: 10.5 + x = 13.793114224 Solving 10.5 + x = 13.793114224 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 = 13.793114224 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 13.793114224 + -10.5 x = 13.793114224 + -10.5 Combine like terms: 13.793114224 + -10.5 = 3.293114224 x = 3.293114224 Simplifying x = 3.293114224Subproblem 2
x + 10.5 = -13.793114224 Simplifying x + 10.5 = -13.793114224 Reorder the terms: 10.5 + x = -13.793114224 Solving 10.5 + x = -13.793114224 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 = -13.793114224 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -13.793114224 + -10.5 x = -13.793114224 + -10.5 Combine like terms: -13.793114224 + -10.5 = -24.293114224 x = -24.293114224 Simplifying x = -24.293114224Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.293114224, -24.293114224}
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