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Simplifying 5x2 + 27x + 24 = 0 Reorder the terms: 24 + 27x + 5x2 = 0 Solving 24 + 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'. 4.8 + 5.4x + x2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + 5.4x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + 5.4x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + 5.4x + x2 = 0 + -4.8 5.4x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 5.4x + x2 = -4.8 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 = -4.8 + 7.29 Reorder the terms: 7.29 + 5.4x + x2 = -4.8 + 7.29 Combine like terms: -4.8 + 7.29 = 2.49 7.29 + 5.4x + x2 = 2.49 Factor a perfect square on the left side: (x + 2.7)(x + 2.7) = 2.49 Calculate the square root of the right side: 1.577973384 Break this problem into two subproblems by setting (x + 2.7) equal to 1.577973384 and -1.577973384.Subproblem 1
x + 2.7 = 1.577973384 Simplifying x + 2.7 = 1.577973384 Reorder the terms: 2.7 + x = 1.577973384 Solving 2.7 + x = 1.577973384 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 = 1.577973384 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 1.577973384 + -2.7 x = 1.577973384 + -2.7 Combine like terms: 1.577973384 + -2.7 = -1.122026616 x = -1.122026616 Simplifying x = -1.122026616Subproblem 2
x + 2.7 = -1.577973384 Simplifying x + 2.7 = -1.577973384 Reorder the terms: 2.7 + x = -1.577973384 Solving 2.7 + x = -1.577973384 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 = -1.577973384 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -1.577973384 + -2.7 x = -1.577973384 + -2.7 Combine like terms: -1.577973384 + -2.7 = -4.277973384 x = -4.277973384 Simplifying x = -4.277973384Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.122026616, -4.277973384}
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