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Simplifying 9x2 + 54x + 79 = 0 Reorder the terms: 79 + 54x + 9x2 = 0 Solving 79 + 54x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 8.777777778 + 6x + x2 = 0 Move the constant term to the right: Add '-8.777777778' to each side of the equation. 8.777777778 + 6x + -8.777777778 + x2 = 0 + -8.777777778 Reorder the terms: 8.777777778 + -8.777777778 + 6x + x2 = 0 + -8.777777778 Combine like terms: 8.777777778 + -8.777777778 = 0.000000000 0.000000000 + 6x + x2 = 0 + -8.777777778 6x + x2 = 0 + -8.777777778 Combine like terms: 0 + -8.777777778 = -8.777777778 6x + x2 = -8.777777778 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -8.777777778 + 9 Reorder the terms: 9 + 6x + x2 = -8.777777778 + 9 Combine like terms: -8.777777778 + 9 = 0.222222222 9 + 6x + x2 = 0.222222222 Factor a perfect square on the left side: (x + 3)(x + 3) = 0.222222222 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (x + 3) equal to 0.471404521 and -0.471404521.Subproblem 1
x + 3 = 0.471404521 Simplifying x + 3 = 0.471404521 Reorder the terms: 3 + x = 0.471404521 Solving 3 + x = 0.471404521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0.471404521 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0.471404521 + -3 x = 0.471404521 + -3 Combine like terms: 0.471404521 + -3 = -2.528595479 x = -2.528595479 Simplifying x = -2.528595479Subproblem 2
x + 3 = -0.471404521 Simplifying x + 3 = -0.471404521 Reorder the terms: 3 + x = -0.471404521 Solving 3 + x = -0.471404521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -0.471404521 + -3 Combine like terms: 3 + -3 = 0 0 + x = -0.471404521 + -3 x = -0.471404521 + -3 Combine like terms: -0.471404521 + -3 = -3.471404521 x = -3.471404521 Simplifying x = -3.471404521Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.528595479, -3.471404521}
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