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Simplifying 10x2 + -27x + -800 = 1980 Reorder the terms: -800 + -27x + 10x2 = 1980 Solving -800 + -27x + 10x2 = 1980 Solving for variable 'x'. Reorder the terms: -800 + -1980 + -27x + 10x2 = 1980 + -1980 Combine like terms: -800 + -1980 = -2780 -2780 + -27x + 10x2 = 1980 + -1980 Combine like terms: 1980 + -1980 = 0 -2780 + -27x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -278 + -2.7x + x2 = 0 Move the constant term to the right: Add '278' to each side of the equation. -278 + -2.7x + 278 + x2 = 0 + 278 Reorder the terms: -278 + 278 + -2.7x + x2 = 0 + 278 Combine like terms: -278 + 278 = 0 0 + -2.7x + x2 = 0 + 278 -2.7x + x2 = 0 + 278 Combine like terms: 0 + 278 = 278 -2.7x + x2 = 278 The x term is -2.7x. Take half its coefficient (-1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. -2.7x + 1.8225 + x2 = 278 + 1.8225 Reorder the terms: 1.8225 + -2.7x + x2 = 278 + 1.8225 Combine like terms: 278 + 1.8225 = 279.8225 1.8225 + -2.7x + x2 = 279.8225 Factor a perfect square on the left side: (x + -1.35)(x + -1.35) = 279.8225 Calculate the square root of the right side: 16.727895863 Break this problem into two subproblems by setting (x + -1.35) equal to 16.727895863 and -16.727895863.Subproblem 1
x + -1.35 = 16.727895863 Simplifying x + -1.35 = 16.727895863 Reorder the terms: -1.35 + x = 16.727895863 Solving -1.35 + x = 16.727895863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = 16.727895863 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = 16.727895863 + 1.35 x = 16.727895863 + 1.35 Combine like terms: 16.727895863 + 1.35 = 18.077895863 x = 18.077895863 Simplifying x = 18.077895863Subproblem 2
x + -1.35 = -16.727895863 Simplifying x + -1.35 = -16.727895863 Reorder the terms: -1.35 + x = -16.727895863 Solving -1.35 + x = -16.727895863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = -16.727895863 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = -16.727895863 + 1.35 x = -16.727895863 + 1.35 Combine like terms: -16.727895863 + 1.35 = -15.377895863 x = -15.377895863 Simplifying x = -15.377895863Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.077895863, -15.377895863}
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