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Simplifying 5x2 + 27x + -16 = 0 Reorder the terms: -16 + 27x + 5x2 = 0 Solving -16 + 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'. -3.2 + 5.4x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 5.4x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 5.4x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 5.4x + x2 = 0 + 3.2 5.4x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 5.4x + x2 = 3.2 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 = 3.2 + 7.29 Reorder the terms: 7.29 + 5.4x + x2 = 3.2 + 7.29 Combine like terms: 3.2 + 7.29 = 10.49 7.29 + 5.4x + x2 = 10.49 Factor a perfect square on the left side: (x + 2.7)(x + 2.7) = 10.49 Calculate the square root of the right side: 3.238826948 Break this problem into two subproblems by setting (x + 2.7) equal to 3.238826948 and -3.238826948.Subproblem 1
x + 2.7 = 3.238826948 Simplifying x + 2.7 = 3.238826948 Reorder the terms: 2.7 + x = 3.238826948 Solving 2.7 + x = 3.238826948 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 = 3.238826948 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 3.238826948 + -2.7 x = 3.238826948 + -2.7 Combine like terms: 3.238826948 + -2.7 = 0.538826948 x = 0.538826948 Simplifying x = 0.538826948Subproblem 2
x + 2.7 = -3.238826948 Simplifying x + 2.7 = -3.238826948 Reorder the terms: 2.7 + x = -3.238826948 Solving 2.7 + x = -3.238826948 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 = -3.238826948 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -3.238826948 + -2.7 x = -3.238826948 + -2.7 Combine like terms: -3.238826948 + -2.7 = -5.938826948 x = -5.938826948 Simplifying x = -5.938826948Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.538826948, -5.938826948}
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