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Simplifying 9x2 + 28x + -34 = 6 Reorder the terms: -34 + 28x + 9x2 = 6 Solving -34 + 28x + 9x2 = 6 Solving for variable 'x'. Reorder the terms: -34 + -6 + 28x + 9x2 = 6 + -6 Combine like terms: -34 + -6 = -40 -40 + 28x + 9x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -40 + 28x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.444444444 + 3.111111111x + x2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + 3.111111111x + 4.444444444 + x2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + 3.111111111x + x2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + 3.111111111x + x2 = 0 + 4.444444444 3.111111111x + x2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 3.111111111x + x2 = 4.444444444 The x term is 3.111111111x. Take half its coefficient (1.555555556). Square it (2.419753088) and add it to both sides. Add '2.419753088' to each side of the equation. 3.111111111x + 2.419753088 + x2 = 4.444444444 + 2.419753088 Reorder the terms: 2.419753088 + 3.111111111x + x2 = 4.444444444 + 2.419753088 Combine like terms: 4.444444444 + 2.419753088 = 6.864197532 2.419753088 + 3.111111111x + x2 = 6.864197532 Factor a perfect square on the left side: (x + 1.555555556)(x + 1.555555556) = 6.864197532 Calculate the square root of the right side: 2.619961361 Break this problem into two subproblems by setting (x + 1.555555556) equal to 2.619961361 and -2.619961361.Subproblem 1
x + 1.555555556 = 2.619961361 Simplifying x + 1.555555556 = 2.619961361 Reorder the terms: 1.555555556 + x = 2.619961361 Solving 1.555555556 + x = 2.619961361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.555555556' to each side of the equation. 1.555555556 + -1.555555556 + x = 2.619961361 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = 2.619961361 + -1.555555556 x = 2.619961361 + -1.555555556 Combine like terms: 2.619961361 + -1.555555556 = 1.064405805 x = 1.064405805 Simplifying x = 1.064405805Subproblem 2
x + 1.555555556 = -2.619961361 Simplifying x + 1.555555556 = -2.619961361 Reorder the terms: 1.555555556 + x = -2.619961361 Solving 1.555555556 + x = -2.619961361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.555555556' to each side of the equation. 1.555555556 + -1.555555556 + x = -2.619961361 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = -2.619961361 + -1.555555556 x = -2.619961361 + -1.555555556 Combine like terms: -2.619961361 + -1.555555556 = -4.175516917 x = -4.175516917 Simplifying x = -4.175516917Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.064405805, -4.175516917}
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