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Simplifying 9x2 + 18x + -55 = 6 Reorder the terms: -55 + 18x + 9x2 = 6 Solving -55 + 18x + 9x2 = 6 Solving for variable 'x'. Reorder the terms: -55 + -6 + 18x + 9x2 = 6 + -6 Combine like terms: -55 + -6 = -61 -61 + 18x + 9x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -61 + 18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.777777778 + 2x + x2 = 0 Move the constant term to the right: Add '6.777777778' to each side of the equation. -6.777777778 + 2x + 6.777777778 + x2 = 0 + 6.777777778 Reorder the terms: -6.777777778 + 6.777777778 + 2x + x2 = 0 + 6.777777778 Combine like terms: -6.777777778 + 6.777777778 = 0.000000000 0.000000000 + 2x + x2 = 0 + 6.777777778 2x + x2 = 0 + 6.777777778 Combine like terms: 0 + 6.777777778 = 6.777777778 2x + x2 = 6.777777778 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 6.777777778 + 1 Reorder the terms: 1 + 2x + x2 = 6.777777778 + 1 Combine like terms: 6.777777778 + 1 = 7.777777778 1 + 2x + x2 = 7.777777778 Factor a perfect square on the left side: (x + 1)(x + 1) = 7.777777778 Calculate the square root of the right side: 2.788866755 Break this problem into two subproblems by setting (x + 1) equal to 2.788866755 and -2.788866755.Subproblem 1
x + 1 = 2.788866755 Simplifying x + 1 = 2.788866755 Reorder the terms: 1 + x = 2.788866755 Solving 1 + x = 2.788866755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.788866755 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.788866755 + -1 x = 2.788866755 + -1 Combine like terms: 2.788866755 + -1 = 1.788866755 x = 1.788866755 Simplifying x = 1.788866755Subproblem 2
x + 1 = -2.788866755 Simplifying x + 1 = -2.788866755 Reorder the terms: 1 + x = -2.788866755 Solving 1 + x = -2.788866755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.788866755 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.788866755 + -1 x = -2.788866755 + -1 Combine like terms: -2.788866755 + -1 = -3.788866755 x = -3.788866755 Simplifying x = -3.788866755Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.788866755, -3.788866755}
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