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Simplifying 8x2 + -72x + 27 = 0 Reorder the terms: 27 + -72x + 8x2 = 0 Solving 27 + -72x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.375 + -9x + x2 = 0 Move the constant term to the right: Add '-3.375' to each side of the equation. 3.375 + -9x + -3.375 + x2 = 0 + -3.375 Reorder the terms: 3.375 + -3.375 + -9x + x2 = 0 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + -9x + x2 = 0 + -3.375 -9x + x2 = 0 + -3.375 Combine like terms: 0 + -3.375 = -3.375 -9x + x2 = -3.375 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -3.375 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -3.375 + 20.25 Combine like terms: -3.375 + 20.25 = 16.875 20.25 + -9x + x2 = 16.875 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 16.875 Calculate the square root of the right side: 4.107919181 Break this problem into two subproblems by setting (x + -4.5) equal to 4.107919181 and -4.107919181.Subproblem 1
x + -4.5 = 4.107919181 Simplifying x + -4.5 = 4.107919181 Reorder the terms: -4.5 + x = 4.107919181 Solving -4.5 + x = 4.107919181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.107919181 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.107919181 + 4.5 x = 4.107919181 + 4.5 Combine like terms: 4.107919181 + 4.5 = 8.607919181 x = 8.607919181 Simplifying x = 8.607919181Subproblem 2
x + -4.5 = -4.107919181 Simplifying x + -4.5 = -4.107919181 Reorder the terms: -4.5 + x = -4.107919181 Solving -4.5 + x = -4.107919181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.107919181 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.107919181 + 4.5 x = -4.107919181 + 4.5 Combine like terms: -4.107919181 + 4.5 = 0.392080819 x = 0.392080819 Simplifying x = 0.392080819Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.607919181, 0.392080819}
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