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Simplifying x(x + 6) = 294 Reorder the terms: x(6 + x) = 294 (6 * x + x * x) = 294 (6x + x2) = 294 Solving 6x + x2 = 294 Solving for variable 'x'. Reorder the terms: -294 + 6x + x2 = 294 + -294 Combine like terms: 294 + -294 = 0 -294 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '294' to each side of the equation. -294 + 6x + 294 + x2 = 0 + 294 Reorder the terms: -294 + 294 + 6x + x2 = 0 + 294 Combine like terms: -294 + 294 = 0 0 + 6x + x2 = 0 + 294 6x + x2 = 0 + 294 Combine like terms: 0 + 294 = 294 6x + x2 = 294 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 = 294 + 9 Reorder the terms: 9 + 6x + x2 = 294 + 9 Combine like terms: 294 + 9 = 303 9 + 6x + x2 = 303 Factor a perfect square on the left side: (x + 3)(x + 3) = 303 Calculate the square root of the right side: 17.406895186 Break this problem into two subproblems by setting (x + 3) equal to 17.406895186 and -17.406895186.Subproblem 1
x + 3 = 17.406895186 Simplifying x + 3 = 17.406895186 Reorder the terms: 3 + x = 17.406895186 Solving 3 + x = 17.406895186 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 = 17.406895186 + -3 Combine like terms: 3 + -3 = 0 0 + x = 17.406895186 + -3 x = 17.406895186 + -3 Combine like terms: 17.406895186 + -3 = 14.406895186 x = 14.406895186 Simplifying x = 14.406895186Subproblem 2
x + 3 = -17.406895186 Simplifying x + 3 = -17.406895186 Reorder the terms: 3 + x = -17.406895186 Solving 3 + x = -17.406895186 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 = -17.406895186 + -3 Combine like terms: 3 + -3 = 0 0 + x = -17.406895186 + -3 x = -17.406895186 + -3 Combine like terms: -17.406895186 + -3 = -20.406895186 x = -20.406895186 Simplifying x = -20.406895186Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.406895186, -20.406895186}
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