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Simplifying 8x2 + -40x + 27 = 0 Reorder the terms: 27 + -40x + 8x2 = 0 Solving 27 + -40x + 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 + -5x + x2 = 0 Move the constant term to the right: Add '-3.375' to each side of the equation. 3.375 + -5x + -3.375 + x2 = 0 + -3.375 Reorder the terms: 3.375 + -3.375 + -5x + x2 = 0 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + -5x + x2 = 0 + -3.375 -5x + x2 = 0 + -3.375 Combine like terms: 0 + -3.375 = -3.375 -5x + x2 = -3.375 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -3.375 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3.375 + 6.25 Combine like terms: -3.375 + 6.25 = 2.875 6.25 + -5x + x2 = 2.875 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + -2.5) equal to 1.695582496 and -1.695582496.Subproblem 1
x + -2.5 = 1.695582496 Simplifying x + -2.5 = 1.695582496 Reorder the terms: -2.5 + x = 1.695582496 Solving -2.5 + x = 1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.695582496 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.695582496 + 2.5 x = 1.695582496 + 2.5 Combine like terms: 1.695582496 + 2.5 = 4.195582496 x = 4.195582496 Simplifying x = 4.195582496Subproblem 2
x + -2.5 = -1.695582496 Simplifying x + -2.5 = -1.695582496 Reorder the terms: -2.5 + x = -1.695582496 Solving -2.5 + x = -1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.695582496 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.695582496 + 2.5 x = -1.695582496 + 2.5 Combine like terms: -1.695582496 + 2.5 = 0.804417504 x = 0.804417504 Simplifying x = 0.804417504Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.195582496, 0.804417504}
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