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Simplifying x2 + x2 + 6x + 9 = 900 Reorder the terms: 9 + 6x + x2 + x2 = 900 Combine like terms: x2 + x2 = 2x2 9 + 6x + 2x2 = 900 Solving 9 + 6x + 2x2 = 900 Solving for variable 'x'. Reorder the terms: 9 + -900 + 6x + 2x2 = 900 + -900 Combine like terms: 9 + -900 = -891 -891 + 6x + 2x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -891 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -445.5 + 3x + x2 = 0 Move the constant term to the right: Add '445.5' to each side of the equation. -445.5 + 3x + 445.5 + x2 = 0 + 445.5 Reorder the terms: -445.5 + 445.5 + 3x + x2 = 0 + 445.5 Combine like terms: -445.5 + 445.5 = 0.0 0.0 + 3x + x2 = 0 + 445.5 3x + x2 = 0 + 445.5 Combine like terms: 0 + 445.5 = 445.5 3x + x2 = 445.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 445.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 445.5 + 2.25 Combine like terms: 445.5 + 2.25 = 447.75 2.25 + 3x + x2 = 447.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 447.75 Calculate the square root of the right side: 21.160103969 Break this problem into two subproblems by setting (x + 1.5) equal to 21.160103969 and -21.160103969.Subproblem 1
x + 1.5 = 21.160103969 Simplifying x + 1.5 = 21.160103969 Reorder the terms: 1.5 + x = 21.160103969 Solving 1.5 + x = 21.160103969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 21.160103969 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 21.160103969 + -1.5 x = 21.160103969 + -1.5 Combine like terms: 21.160103969 + -1.5 = 19.660103969 x = 19.660103969 Simplifying x = 19.660103969Subproblem 2
x + 1.5 = -21.160103969 Simplifying x + 1.5 = -21.160103969 Reorder the terms: 1.5 + x = -21.160103969 Solving 1.5 + x = -21.160103969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -21.160103969 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -21.160103969 + -1.5 x = -21.160103969 + -1.5 Combine like terms: -21.160103969 + -1.5 = -22.660103969 x = -22.660103969 Simplifying x = -22.660103969Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.660103969, -22.660103969}
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