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Simplifying x2 + 6x + -225 = 0 Reorder the terms: -225 + 6x + x2 = 0 Solving -225 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 6x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 6x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 6x + x2 = 0 + 225 6x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 6x + x2 = 225 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 = 225 + 9 Reorder the terms: 9 + 6x + x2 = 225 + 9 Combine like terms: 225 + 9 = 234 9 + 6x + x2 = 234 Factor a perfect square on the left side: (x + 3)(x + 3) = 234 Calculate the square root of the right side: 15.297058541 Break this problem into two subproblems by setting (x + 3) equal to 15.297058541 and -15.297058541.Subproblem 1
x + 3 = 15.297058541 Simplifying x + 3 = 15.297058541 Reorder the terms: 3 + x = 15.297058541 Solving 3 + x = 15.297058541 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 = 15.297058541 + -3 Combine like terms: 3 + -3 = 0 0 + x = 15.297058541 + -3 x = 15.297058541 + -3 Combine like terms: 15.297058541 + -3 = 12.297058541 x = 12.297058541 Simplifying x = 12.297058541Subproblem 2
x + 3 = -15.297058541 Simplifying x + 3 = -15.297058541 Reorder the terms: 3 + x = -15.297058541 Solving 3 + x = -15.297058541 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 = -15.297058541 + -3 Combine like terms: 3 + -3 = 0 0 + x = -15.297058541 + -3 x = -15.297058541 + -3 Combine like terms: -15.297058541 + -3 = -18.297058541 x = -18.297058541 Simplifying x = -18.297058541Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.297058541, -18.297058541}
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