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Simplifying x2 + -9x + -900 = 0 Reorder the terms: -900 + -9x + x2 = 0 Solving -900 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + -9x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + -9x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + -9x + x2 = 0 + 900 -9x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 -9x + x2 = 900 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 = 900 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 900 + 20.25 Combine like terms: 900 + 20.25 = 920.25 20.25 + -9x + x2 = 920.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 920.25 Calculate the square root of the right side: 30.335622624 Break this problem into two subproblems by setting (x + -4.5) equal to 30.335622624 and -30.335622624.Subproblem 1
x + -4.5 = 30.335622624 Simplifying x + -4.5 = 30.335622624 Reorder the terms: -4.5 + x = 30.335622624 Solving -4.5 + x = 30.335622624 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 = 30.335622624 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 30.335622624 + 4.5 x = 30.335622624 + 4.5 Combine like terms: 30.335622624 + 4.5 = 34.835622624 x = 34.835622624 Simplifying x = 34.835622624Subproblem 2
x + -4.5 = -30.335622624 Simplifying x + -4.5 = -30.335622624 Reorder the terms: -4.5 + x = -30.335622624 Solving -4.5 + x = -30.335622624 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 = -30.335622624 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -30.335622624 + 4.5 x = -30.335622624 + 4.5 Combine like terms: -30.335622624 + 4.5 = -25.835622624 x = -25.835622624 Simplifying x = -25.835622624Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.835622624, -25.835622624}
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