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Simplifying 9x2 + 27x + -488 = 0 Reorder the terms: -488 + 27x + 9x2 = 0 Solving -488 + 27x + 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'. -54.22222222 + 3x + x2 = 0 Move the constant term to the right: Add '54.22222222' to each side of the equation. -54.22222222 + 3x + 54.22222222 + x2 = 0 + 54.22222222 Reorder the terms: -54.22222222 + 54.22222222 + 3x + x2 = 0 + 54.22222222 Combine like terms: -54.22222222 + 54.22222222 = 0.00000000 0.00000000 + 3x + x2 = 0 + 54.22222222 3x + x2 = 0 + 54.22222222 Combine like terms: 0 + 54.22222222 = 54.22222222 3x + x2 = 54.22222222 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 54.22222222 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 54.22222222 + 2.25 Combine like terms: 54.22222222 + 2.25 = 56.47222222 2.25 + 3x + x2 = 56.47222222 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 56.47222222 Calculate the square root of the right side: 7.514800212 Break this problem into two subproblems by setting (x + 1.5) equal to 7.514800212 and -7.514800212.Subproblem 1
x + 1.5 = 7.514800212 Simplifying x + 1.5 = 7.514800212 Reorder the terms: 1.5 + x = 7.514800212 Solving 1.5 + x = 7.514800212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.514800212 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.514800212 + -1.5 x = 7.514800212 + -1.5 Combine like terms: 7.514800212 + -1.5 = 6.014800212 x = 6.014800212 Simplifying x = 6.014800212Subproblem 2
x + 1.5 = -7.514800212 Simplifying x + 1.5 = -7.514800212 Reorder the terms: 1.5 + x = -7.514800212 Solving 1.5 + x = -7.514800212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.514800212 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.514800212 + -1.5 x = -7.514800212 + -1.5 Combine like terms: -7.514800212 + -1.5 = -9.014800212 x = -9.014800212 Simplifying x = -9.014800212Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.014800212, -9.014800212}
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