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Simplifying 10x2 + -36x + 27 = 0 Reorder the terms: 27 + -36x + 10x2 = 0 Solving 27 + -36x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 2.7 + -3.6x + x2 = 0 Move the constant term to the right: Add '-2.7' to each side of the equation. 2.7 + -3.6x + -2.7 + x2 = 0 + -2.7 Reorder the terms: 2.7 + -2.7 + -3.6x + x2 = 0 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + -3.6x + x2 = 0 + -2.7 -3.6x + x2 = 0 + -2.7 Combine like terms: 0 + -2.7 = -2.7 -3.6x + x2 = -2.7 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -2.7 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -2.7 + 3.24 Combine like terms: -2.7 + 3.24 = 0.54 3.24 + -3.6x + x2 = 0.54 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 0.54 Calculate the square root of the right side: 0.734846923 Break this problem into two subproblems by setting (x + -1.8) equal to 0.734846923 and -0.734846923.Subproblem 1
x + -1.8 = 0.734846923 Simplifying x + -1.8 = 0.734846923 Reorder the terms: -1.8 + x = 0.734846923 Solving -1.8 + x = 0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 0.734846923 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 0.734846923 + 1.8 x = 0.734846923 + 1.8 Combine like terms: 0.734846923 + 1.8 = 2.534846923 x = 2.534846923 Simplifying x = 2.534846923Subproblem 2
x + -1.8 = -0.734846923 Simplifying x + -1.8 = -0.734846923 Reorder the terms: -1.8 + x = -0.734846923 Solving -1.8 + x = -0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -0.734846923 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -0.734846923 + 1.8 x = -0.734846923 + 1.8 Combine like terms: -0.734846923 + 1.8 = 1.065153077 x = 1.065153077 Simplifying x = 1.065153077Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.534846923, 1.065153077}
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