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Simplifying 27x2 + -97x + -35 = 0 Reorder the terms: -35 + -97x + 27x2 = 0 Solving -35 + -97x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -1.296296296 + -3.592592593x + x2 = 0 Move the constant term to the right: Add '1.296296296' to each side of the equation. -1.296296296 + -3.592592593x + 1.296296296 + x2 = 0 + 1.296296296 Reorder the terms: -1.296296296 + 1.296296296 + -3.592592593x + x2 = 0 + 1.296296296 Combine like terms: -1.296296296 + 1.296296296 = 0.000000000 0.000000000 + -3.592592593x + x2 = 0 + 1.296296296 -3.592592593x + x2 = 0 + 1.296296296 Combine like terms: 0 + 1.296296296 = 1.296296296 -3.592592593x + x2 = 1.296296296 The x term is -3.592592593x. Take half its coefficient (-1.796296297). Square it (3.226680387) and add it to both sides. Add '3.226680387' to each side of the equation. -3.592592593x + 3.226680387 + x2 = 1.296296296 + 3.226680387 Reorder the terms: 3.226680387 + -3.592592593x + x2 = 1.296296296 + 3.226680387 Combine like terms: 1.296296296 + 3.226680387 = 4.522976683 3.226680387 + -3.592592593x + x2 = 4.522976683 Factor a perfect square on the left side: (x + -1.796296297)(x + -1.796296297) = 4.522976683 Calculate the square root of the right side: 2.126729104 Break this problem into two subproblems by setting (x + -1.796296297) equal to 2.126729104 and -2.126729104.Subproblem 1
x + -1.796296297 = 2.126729104 Simplifying x + -1.796296297 = 2.126729104 Reorder the terms: -1.796296297 + x = 2.126729104 Solving -1.796296297 + x = 2.126729104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.796296297' to each side of the equation. -1.796296297 + 1.796296297 + x = 2.126729104 + 1.796296297 Combine like terms: -1.796296297 + 1.796296297 = 0.000000000 0.000000000 + x = 2.126729104 + 1.796296297 x = 2.126729104 + 1.796296297 Combine like terms: 2.126729104 + 1.796296297 = 3.923025401 x = 3.923025401 Simplifying x = 3.923025401Subproblem 2
x + -1.796296297 = -2.126729104 Simplifying x + -1.796296297 = -2.126729104 Reorder the terms: -1.796296297 + x = -2.126729104 Solving -1.796296297 + x = -2.126729104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.796296297' to each side of the equation. -1.796296297 + 1.796296297 + x = -2.126729104 + 1.796296297 Combine like terms: -1.796296297 + 1.796296297 = 0.000000000 0.000000000 + x = -2.126729104 + 1.796296297 x = -2.126729104 + 1.796296297 Combine like terms: -2.126729104 + 1.796296297 = -0.330432807 x = -0.330432807 Simplifying x = -0.330432807Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.923025401, -0.330432807}
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