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Simplifying 8x2 + -32x + 9 = 0 Reorder the terms: 9 + -32x + 8x2 = 0 Solving 9 + -32x + 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'. 1.125 + -4x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -4x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -4x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -4x + x2 = 0 + -1.125 -4x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -4x + x2 = -1.125 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1.125 + 4 Reorder the terms: 4 + -4x + x2 = -1.125 + 4 Combine like terms: -1.125 + 4 = 2.875 4 + -4x + x2 = 2.875 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + -2) equal to 1.695582496 and -1.695582496.Subproblem 1
x + -2 = 1.695582496 Simplifying x + -2 = 1.695582496 Reorder the terms: -2 + x = 1.695582496 Solving -2 + x = 1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.695582496 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.695582496 + 2 x = 1.695582496 + 2 Combine like terms: 1.695582496 + 2 = 3.695582496 x = 3.695582496 Simplifying x = 3.695582496Subproblem 2
x + -2 = -1.695582496 Simplifying x + -2 = -1.695582496 Reorder the terms: -2 + x = -1.695582496 Solving -2 + x = -1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.695582496 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.695582496 + 2 x = -1.695582496 + 2 Combine like terms: -1.695582496 + 2 = 0.304417504 x = 0.304417504 Simplifying x = 0.304417504Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.695582496, 0.304417504}
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