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Simplifying 6x2 + -27x + 28 = 0 Reorder the terms: 28 + -27x + 6x2 = 0 Solving 28 + -27x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 4.666666667 + -4.5x + x2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + -4.5x + -4.666666667 + x2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + -4.5x + x2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + -4.5x + x2 = 0 + -4.666666667 -4.5x + x2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 -4.5x + x2 = -4.666666667 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -4.666666667 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -4.666666667 + 5.0625 Combine like terms: -4.666666667 + 5.0625 = 0.395833333 5.0625 + -4.5x + x2 = 0.395833333 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 0.395833333 Calculate the square root of the right side: 0.629152869 Break this problem into two subproblems by setting (x + -2.25) equal to 0.629152869 and -0.629152869.Subproblem 1
x + -2.25 = 0.629152869 Simplifying x + -2.25 = 0.629152869 Reorder the terms: -2.25 + x = 0.629152869 Solving -2.25 + x = 0.629152869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 0.629152869 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 0.629152869 + 2.25 x = 0.629152869 + 2.25 Combine like terms: 0.629152869 + 2.25 = 2.879152869 x = 2.879152869 Simplifying x = 2.879152869Subproblem 2
x + -2.25 = -0.629152869 Simplifying x + -2.25 = -0.629152869 Reorder the terms: -2.25 + x = -0.629152869 Solving -2.25 + x = -0.629152869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -0.629152869 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -0.629152869 + 2.25 x = -0.629152869 + 2.25 Combine like terms: -0.629152869 + 2.25 = 1.620847131 x = 1.620847131 Simplifying x = 1.620847131Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.879152869, 1.620847131}
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