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Simplifying x2 + -9x + -48 = 0 Reorder the terms: -48 + -9x + x2 = 0 Solving -48 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -9x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -9x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -9x + x2 = 0 + 48 -9x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -9x + x2 = 48 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 = 48 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 48 + 20.25 Combine like terms: 48 + 20.25 = 68.25 20.25 + -9x + x2 = 68.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + -4.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + -4.5 = 8.261355821 Simplifying x + -4.5 = 8.261355821 Reorder the terms: -4.5 + x = 8.261355821 Solving -4.5 + x = 8.261355821 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 = 8.261355821 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 8.261355821 + 4.5 x = 8.261355821 + 4.5 Combine like terms: 8.261355821 + 4.5 = 12.761355821 x = 12.761355821 Simplifying x = 12.761355821Subproblem 2
x + -4.5 = -8.261355821 Simplifying x + -4.5 = -8.261355821 Reorder the terms: -4.5 + x = -8.261355821 Solving -4.5 + x = -8.261355821 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 = -8.261355821 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -8.261355821 + 4.5 x = -8.261355821 + 4.5 Combine like terms: -8.261355821 + 4.5 = -3.761355821 x = -3.761355821 Simplifying x = -3.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.761355821, -3.761355821}
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