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Simplifying x(x + -9) = 21 Reorder the terms: x(-9 + x) = 21 (-9 * x + x * x) = 21 (-9x + x2) = 21 Solving -9x + x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + -9x + x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -9x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -9x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -9x + x2 = 0 + 21 -9x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -9x + x2 = 21 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 = 21 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 21 + 20.25 Combine like terms: 21 + 20.25 = 41.25 20.25 + -9x + x2 = 41.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + -4.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + -4.5 = 6.422616289 Simplifying x + -4.5 = 6.422616289 Reorder the terms: -4.5 + x = 6.422616289 Solving -4.5 + x = 6.422616289 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 = 6.422616289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.422616289 + 4.5 x = 6.422616289 + 4.5 Combine like terms: 6.422616289 + 4.5 = 10.922616289 x = 10.922616289 Simplifying x = 10.922616289Subproblem 2
x + -4.5 = -6.422616289 Simplifying x + -4.5 = -6.422616289 Reorder the terms: -4.5 + x = -6.422616289 Solving -4.5 + x = -6.422616289 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 = -6.422616289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.422616289 + 4.5 x = -6.422616289 + 4.5 Combine like terms: -6.422616289 + 4.5 = -1.922616289 x = -1.922616289 Simplifying x = -1.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.922616289, -1.922616289}
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