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Simplifying x2 + 6x + -450 = 0 Reorder the terms: -450 + 6x + x2 = 0 Solving -450 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 6x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 6x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 6x + x2 = 0 + 450 6x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 6x + x2 = 450 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 = 450 + 9 Reorder the terms: 9 + 6x + x2 = 450 + 9 Combine like terms: 450 + 9 = 459 9 + 6x + x2 = 459 Factor a perfect square on the left side: (x + 3)(x + 3) = 459 Calculate the square root of the right side: 21.424285286 Break this problem into two subproblems by setting (x + 3) equal to 21.424285286 and -21.424285286.Subproblem 1
x + 3 = 21.424285286 Simplifying x + 3 = 21.424285286 Reorder the terms: 3 + x = 21.424285286 Solving 3 + x = 21.424285286 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 = 21.424285286 + -3 Combine like terms: 3 + -3 = 0 0 + x = 21.424285286 + -3 x = 21.424285286 + -3 Combine like terms: 21.424285286 + -3 = 18.424285286 x = 18.424285286 Simplifying x = 18.424285286Subproblem 2
x + 3 = -21.424285286 Simplifying x + 3 = -21.424285286 Reorder the terms: 3 + x = -21.424285286 Solving 3 + x = -21.424285286 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 = -21.424285286 + -3 Combine like terms: 3 + -3 = 0 0 + x = -21.424285286 + -3 x = -21.424285286 + -3 Combine like terms: -21.424285286 + -3 = -24.424285286 x = -24.424285286 Simplifying x = -24.424285286Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.424285286, -24.424285286}
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