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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 = 4.09 7.29 + -5.4x + x2 = 4.09 Factor a perfect square on the left side: (x + -2.7)(x + -2.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + -2.7) equal to 2.022374842 and -2.022374842.Subproblem 1
x + -2.7 = 2.022374842 Simplifying x + -2.7 = 2.022374842 Reorder the terms: -2.7 + x = 2.022374842 Solving -2.7 + x = 2.022374842 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 = 2.022374842 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = 2.022374842 + 2.7 x = 2.022374842 + 2.7 Combine like terms: 2.022374842 + 2.7 = 4.722374842 x = 4.722374842 Simplifying x = 4.722374842Subproblem 2
x + -2.7 = -2.022374842 Simplifying x + -2.7 = -2.022374842 Reorder the terms: -2.7 + x = -2.022374842 Solving -2.7 + x = -2.022374842 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 = -2.022374842 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = -2.022374842 + 2.7 x = -2.022374842 + 2.7 Combine like terms: -2.022374842 + 2.7 = 0.677625158 x = 0.677625158 Simplifying x = 0.677625158Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.722374842, 0.677625158}
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