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Simplifying 5x2 + 54x + 135 = 0 Reorder the terms: 135 + 54x + 5x2 = 0 Solving 135 + 54x + 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'. 27 + 10.8x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + 10.8x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 10.8x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 10.8x + x2 = 0 + -27 10.8x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 10.8x + x2 = -27 The x term is 10.8x. Take half its coefficient (5.4). Square it (29.16) and add it to both sides. Add '29.16' to each side of the equation. 10.8x + 29.16 + x2 = -27 + 29.16 Reorder the terms: 29.16 + 10.8x + x2 = -27 + 29.16 Combine like terms: -27 + 29.16 = 2.16 29.16 + 10.8x + x2 = 2.16 Factor a perfect square on the left side: (x + 5.4)(x + 5.4) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (x + 5.4) equal to 1.469693846 and -1.469693846.Subproblem 1
x + 5.4 = 1.469693846 Simplifying x + 5.4 = 1.469693846 Reorder the terms: 5.4 + x = 1.469693846 Solving 5.4 + x = 1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.4' to each side of the equation. 5.4 + -5.4 + x = 1.469693846 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + x = 1.469693846 + -5.4 x = 1.469693846 + -5.4 Combine like terms: 1.469693846 + -5.4 = -3.930306154 x = -3.930306154 Simplifying x = -3.930306154Subproblem 2
x + 5.4 = -1.469693846 Simplifying x + 5.4 = -1.469693846 Reorder the terms: 5.4 + x = -1.469693846 Solving 5.4 + x = -1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.4' to each side of the equation. 5.4 + -5.4 + x = -1.469693846 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + x = -1.469693846 + -5.4 x = -1.469693846 + -5.4 Combine like terms: -1.469693846 + -5.4 = -6.869693846 x = -6.869693846 Simplifying x = -6.869693846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.930306154, -6.869693846}
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