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Simplifying -1x(x + -8) + 2(x + 2) = x + 9 Reorder the terms: -1x(-8 + x) + 2(x + 2) = x + 9 (-8 * -1x + x * -1x) + 2(x + 2) = x + 9 (8x + -1x2) + 2(x + 2) = x + 9 Reorder the terms: 8x + -1x2 + 2(2 + x) = x + 9 8x + -1x2 + (2 * 2 + x * 2) = x + 9 8x + -1x2 + (4 + 2x) = x + 9 Reorder the terms: 4 + 8x + 2x + -1x2 = x + 9 Combine like terms: 8x + 2x = 10x 4 + 10x + -1x2 = x + 9 Reorder the terms: 4 + 10x + -1x2 = 9 + x Solving 4 + 10x + -1x2 = 9 + x Solving for variable 'x'. Reorder the terms: 4 + -9 + 10x + -1x + -1x2 = 9 + x + -9 + -1x Combine like terms: 4 + -9 = -5 -5 + 10x + -1x + -1x2 = 9 + x + -9 + -1x Combine like terms: 10x + -1x = 9x -5 + 9x + -1x2 = 9 + x + -9 + -1x Reorder the terms: -5 + 9x + -1x2 = 9 + -9 + x + -1x Combine like terms: 9 + -9 = 0 -5 + 9x + -1x2 = 0 + x + -1x -5 + 9x + -1x2 = x + -1x Combine like terms: x + -1x = 0 -5 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -9x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -9x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -9x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9x + x2 = 0 + -5 -9x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -9x + x2 = -5 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 = -5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -5 + 20.25 Combine like terms: -5 + 20.25 = 15.25 20.25 + -9x + x2 = 15.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -4.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -4.5 = 3.905124838 Simplifying x + -4.5 = 3.905124838 Reorder the terms: -4.5 + x = 3.905124838 Solving -4.5 + x = 3.905124838 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 = 3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.905124838 + 4.5 x = 3.905124838 + 4.5 Combine like terms: 3.905124838 + 4.5 = 8.405124838 x = 8.405124838 Simplifying x = 8.405124838Subproblem 2
x + -4.5 = -3.905124838 Simplifying x + -4.5 = -3.905124838 Reorder the terms: -4.5 + x = -3.905124838 Solving -4.5 + x = -3.905124838 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 = -3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.905124838 + 4.5 x = -3.905124838 + 4.5 Combine like terms: -3.905124838 + 4.5 = 0.594875162 x = 0.594875162 Simplifying x = 0.594875162Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.405124838, 0.594875162}
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