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Simplifying 5x2 + -27x + -36 = 0 Reorder the terms: -36 + -27x + 5x2 = 0 Solving -36 + -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'. -7.2 + -5.4x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -5.4x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -5.4x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -5.4x + x2 = 0 + 7.2 -5.4x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -5.4x + x2 = 7.2 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 = 7.2 + 7.29 Reorder the terms: 7.29 + -5.4x + x2 = 7.2 + 7.29 Combine like terms: 7.2 + 7.29 = 14.49 7.29 + -5.4x + x2 = 14.49 Factor a perfect square on the left side: (x + -2.7)(x + -2.7) = 14.49 Calculate the square root of the right side: 3.806573262 Break this problem into two subproblems by setting (x + -2.7) equal to 3.806573262 and -3.806573262.Subproblem 1
x + -2.7 = 3.806573262 Simplifying x + -2.7 = 3.806573262 Reorder the terms: -2.7 + x = 3.806573262 Solving -2.7 + x = 3.806573262 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 = 3.806573262 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = 3.806573262 + 2.7 x = 3.806573262 + 2.7 Combine like terms: 3.806573262 + 2.7 = 6.506573262 x = 6.506573262 Simplifying x = 6.506573262Subproblem 2
x + -2.7 = -3.806573262 Simplifying x + -2.7 = -3.806573262 Reorder the terms: -2.7 + x = -3.806573262 Solving -2.7 + x = -3.806573262 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 = -3.806573262 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = -3.806573262 + 2.7 x = -3.806573262 + 2.7 Combine like terms: -3.806573262 + 2.7 = -1.106573262 x = -1.106573262 Simplifying x = -1.106573262Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.506573262, -1.106573262}
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