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Simplifying 4x2 + -48x + 27 = 0 Reorder the terms: 27 + -48x + 4x2 = 0 Solving 27 + -48x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.75 + -12x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -12x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -12x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -12x + x2 = 0 + -6.75 -12x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -12x + x2 = -6.75 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -6.75 + 36 Reorder the terms: 36 + -12x + x2 = -6.75 + 36 Combine like terms: -6.75 + 36 = 29.25 36 + -12x + x2 = 29.25 Factor a perfect square on the left side: (x + -6)(x + -6) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -6) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -6 = 5.408326913 Simplifying x + -6 = 5.408326913 Reorder the terms: -6 + x = 5.408326913 Solving -6 + x = 5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.408326913 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.408326913 + 6 x = 5.408326913 + 6 Combine like terms: 5.408326913 + 6 = 11.408326913 x = 11.408326913 Simplifying x = 11.408326913Subproblem 2
x + -6 = -5.408326913 Simplifying x + -6 = -5.408326913 Reorder the terms: -6 + x = -5.408326913 Solving -6 + x = -5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.408326913 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.408326913 + 6 x = -5.408326913 + 6 Combine like terms: -5.408326913 + 6 = 0.591673087 x = 0.591673087 Simplifying x = 0.591673087Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.408326913, 0.591673087}
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