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Simplifying 5x2 + 27x + -9 = 0 Reorder the terms: -9 + 27x + 5x2 = 0 Solving -9 + 27x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 5.4x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 5.4x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 5.4x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 5.4x + x2 = 0 + 1.8 5.4x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 5.4x + x2 = 1.8 The x term is 5.4x. Take half its coefficient (2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. 5.4x + 7.29 + x2 = 1.8 + 7.29 Reorder the terms: 7.29 + 5.4x + x2 = 1.8 + 7.29 Combine like terms: 1.8 + 7.29 = 9.09 7.29 + 5.4x + x2 = 9.09 Factor a perfect square on the left side: (x + 2.7)(x + 2.7) = 9.09 Calculate the square root of the right side: 3.014962686 Break this problem into two subproblems by setting (x + 2.7) equal to 3.014962686 and -3.014962686.Subproblem 1
x + 2.7 = 3.014962686 Simplifying x + 2.7 = 3.014962686 Reorder the terms: 2.7 + x = 3.014962686 Solving 2.7 + x = 3.014962686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = 3.014962686 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 3.014962686 + -2.7 x = 3.014962686 + -2.7 Combine like terms: 3.014962686 + -2.7 = 0.314962686 x = 0.314962686 Simplifying x = 0.314962686Subproblem 2
x + 2.7 = -3.014962686 Simplifying x + 2.7 = -3.014962686 Reorder the terms: 2.7 + x = -3.014962686 Solving 2.7 + x = -3.014962686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = -3.014962686 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -3.014962686 + -2.7 x = -3.014962686 + -2.7 Combine like terms: -3.014962686 + -2.7 = -5.714962686 x = -5.714962686 Simplifying x = -5.714962686Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.314962686, -5.714962686}
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