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Simplifying -8x + -9 = -8x(x + -9) Reorder the terms: -9 + -8x = -8x(x + -9) Reorder the terms: -9 + -8x = -8x(-9 + x) -9 + -8x = (-9 * -8x + x * -8x) -9 + -8x = (72x + -8x2) Solving -9 + -8x = 72x + -8x2 Solving for variable 'x'. Combine like terms: -8x + -72x = -80x -9 + -80x + 8x2 = 72x + -8x2 + -72x + 8x2 Reorder the terms: -9 + -80x + 8x2 = 72x + -72x + -8x2 + 8x2 Combine like terms: 72x + -72x = 0 -9 + -80x + 8x2 = 0 + -8x2 + 8x2 -9 + -80x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -9 + -80x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -10x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -10x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -10x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -10x + x2 = 0 + 1.125 -10x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -10x + x2 = 1.125 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 1.125 + 25 Reorder the terms: 25 + -10x + x2 = 1.125 + 25 Combine like terms: 1.125 + 25 = 26.125 25 + -10x + x2 = 26.125 Factor a perfect square on the left side: (x + -5)(x + -5) = 26.125 Calculate the square root of the right side: 5.111262075 Break this problem into two subproblems by setting (x + -5) equal to 5.111262075 and -5.111262075.Subproblem 1
x + -5 = 5.111262075 Simplifying x + -5 = 5.111262075 Reorder the terms: -5 + x = 5.111262075 Solving -5 + x = 5.111262075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.111262075 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.111262075 + 5 x = 5.111262075 + 5 Combine like terms: 5.111262075 + 5 = 10.111262075 x = 10.111262075 Simplifying x = 10.111262075Subproblem 2
x + -5 = -5.111262075 Simplifying x + -5 = -5.111262075 Reorder the terms: -5 + x = -5.111262075 Solving -5 + x = -5.111262075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.111262075 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.111262075 + 5 x = -5.111262075 + 5 Combine like terms: -5.111262075 + 5 = -0.111262075 x = -0.111262075 Simplifying x = -0.111262075Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.111262075, -0.111262075}
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