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Simplifying x2 + 6x + 9 = 12.25 Reorder the terms: 9 + 6x + x2 = 12.25 Solving 9 + 6x + x2 = 12.25 Solving for variable 'x'. Reorder the terms: 9 + -12.25 + 6x + x2 = 12.25 + -12.25 Combine like terms: 9 + -12.25 = -3.25 -3.25 + 6x + x2 = 12.25 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 -3.25 + 6x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 6x + 3.25 + x2 = 0.00 + 3.25 Reorder the terms: -3.25 + 3.25 + 6x + x2 = 0.00 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 6x + x2 = 0.00 + 3.25 6x + x2 = 0.00 + 3.25 Combine like terms: 0.00 + 3.25 = 3.25 6x + x2 = 3.25 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 3.25 + 9 Reorder the terms: 9 + 6x + x2 = 3.25 + 9 Combine like terms: 3.25 + 9 = 12.25 9 + 6x + x2 = 12.25 Factor a perfect square on the left side: (x + 3)(x + 3) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + 3) equal to 3.5 and -3.5.Subproblem 1
x + 3 = 3.5 Simplifying x + 3 = 3.5 Reorder the terms: 3 + x = 3.5 Solving 3 + x = 3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.5 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.5 + -3 x = 3.5 + -3 Combine like terms: 3.5 + -3 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 3 = -3.5 Simplifying x + 3 = -3.5 Reorder the terms: 3 + x = -3.5 Solving 3 + x = -3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.5 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.5 + -3 x = -3.5 + -3 Combine like terms: -3.5 + -3 = -6.5 x = -6.5 Simplifying x = -6.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -6.5}
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