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Simplifying 5x2 + 27x + -15 = 0 Reorder the terms: -15 + 27x + 5x2 = 0 Solving -15 + 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'. -3 + 5.4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 5.4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 5.4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5.4x + x2 = 0 + 3 5.4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 5.4x + x2 = 3 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 = 3 + 7.29 Reorder the terms: 7.29 + 5.4x + x2 = 3 + 7.29 Combine like terms: 3 + 7.29 = 10.29 7.29 + 5.4x + x2 = 10.29 Factor a perfect square on the left side: (x + 2.7)(x + 2.7) = 10.29 Calculate the square root of the right side: 3.207802986 Break this problem into two subproblems by setting (x + 2.7) equal to 3.207802986 and -3.207802986.Subproblem 1
x + 2.7 = 3.207802986 Simplifying x + 2.7 = 3.207802986 Reorder the terms: 2.7 + x = 3.207802986 Solving 2.7 + x = 3.207802986 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 = 3.207802986 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 3.207802986 + -2.7 x = 3.207802986 + -2.7 Combine like terms: 3.207802986 + -2.7 = 0.507802986 x = 0.507802986 Simplifying x = 0.507802986Subproblem 2
x + 2.7 = -3.207802986 Simplifying x + 2.7 = -3.207802986 Reorder the terms: 2.7 + x = -3.207802986 Solving 2.7 + x = -3.207802986 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 = -3.207802986 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -3.207802986 + -2.7 x = -3.207802986 + -2.7 Combine like terms: -3.207802986 + -2.7 = -5.907802986 x = -5.907802986 Simplifying x = -5.907802986Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.507802986, -5.907802986}
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