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Simplifying x2 + -9x + -81 = -8 Reorder the terms: -81 + -9x + x2 = -8 Solving -81 + -9x + x2 = -8 Solving for variable 'x'. Reorder the terms: -81 + 8 + -9x + x2 = -8 + 8 Combine like terms: -81 + 8 = -73 -73 + -9x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 -73 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + -9x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + -9x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -9x + x2 = 0 + 73 -9x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 -9x + x2 = 73 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 = 73 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 73 + 20.25 Combine like terms: 73 + 20.25 = 93.25 20.25 + -9x + x2 = 93.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 93.25 Calculate the square root of the right side: 9.656603958 Break this problem into two subproblems by setting (x + -4.5) equal to 9.656603958 and -9.656603958.Subproblem 1
x + -4.5 = 9.656603958 Simplifying x + -4.5 = 9.656603958 Reorder the terms: -4.5 + x = 9.656603958 Solving -4.5 + x = 9.656603958 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 = 9.656603958 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 9.656603958 + 4.5 x = 9.656603958 + 4.5 Combine like terms: 9.656603958 + 4.5 = 14.156603958 x = 14.156603958 Simplifying x = 14.156603958Subproblem 2
x + -4.5 = -9.656603958 Simplifying x + -4.5 = -9.656603958 Reorder the terms: -4.5 + x = -9.656603958 Solving -4.5 + x = -9.656603958 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 = -9.656603958 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -9.656603958 + 4.5 x = -9.656603958 + 4.5 Combine like terms: -9.656603958 + 4.5 = -5.156603958 x = -5.156603958 Simplifying x = -5.156603958Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.156603958, -5.156603958}
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