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Simplifying -2x2 + 84x + -441 = 0 Reorder the terms: -441 + 84x + -2x2 = 0 Solving -441 + 84x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 220.5 + -42x + x2 = 0 Move the constant term to the right: Add '-220.5' to each side of the equation. 220.5 + -42x + -220.5 + x2 = 0 + -220.5 Reorder the terms: 220.5 + -220.5 + -42x + x2 = 0 + -220.5 Combine like terms: 220.5 + -220.5 = 0.0 0.0 + -42x + x2 = 0 + -220.5 -42x + x2 = 0 + -220.5 Combine like terms: 0 + -220.5 = -220.5 -42x + x2 = -220.5 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -220.5 + 441 Reorder the terms: 441 + -42x + x2 = -220.5 + 441 Combine like terms: -220.5 + 441 = 220.5 441 + -42x + x2 = 220.5 Factor a perfect square on the left side: (x + -21)(x + -21) = 220.5 Calculate the square root of the right side: 14.849242405 Break this problem into two subproblems by setting (x + -21) equal to 14.849242405 and -14.849242405.Subproblem 1
x + -21 = 14.849242405 Simplifying x + -21 = 14.849242405 Reorder the terms: -21 + x = 14.849242405 Solving -21 + x = 14.849242405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 14.849242405 + 21 Combine like terms: -21 + 21 = 0 0 + x = 14.849242405 + 21 x = 14.849242405 + 21 Combine like terms: 14.849242405 + 21 = 35.849242405 x = 35.849242405 Simplifying x = 35.849242405Subproblem 2
x + -21 = -14.849242405 Simplifying x + -21 = -14.849242405 Reorder the terms: -21 + x = -14.849242405 Solving -21 + x = -14.849242405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -14.849242405 + 21 Combine like terms: -21 + 21 = 0 0 + x = -14.849242405 + 21 x = -14.849242405 + 21 Combine like terms: -14.849242405 + 21 = 6.150757595 x = 6.150757595 Simplifying x = 6.150757595Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.849242405, 6.150757595}
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