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Simplifying x2 + 6x = 195 Reorder the terms: 6x + x2 = 195 Solving 6x + x2 = 195 Solving for variable 'x'. Reorder the terms: -195 + 6x + x2 = 195 + -195 Combine like terms: 195 + -195 = 0 -195 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '195' to each side of the equation. -195 + 6x + 195 + x2 = 0 + 195 Reorder the terms: -195 + 195 + 6x + x2 = 0 + 195 Combine like terms: -195 + 195 = 0 0 + 6x + x2 = 0 + 195 6x + x2 = 0 + 195 Combine like terms: 0 + 195 = 195 6x + x2 = 195 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 = 195 + 9 Reorder the terms: 9 + 6x + x2 = 195 + 9 Combine like terms: 195 + 9 = 204 9 + 6x + x2 = 204 Factor a perfect square on the left side: (x + 3)(x + 3) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x + 3) equal to 14.282856857 and -14.282856857.Subproblem 1
x + 3 = 14.282856857 Simplifying x + 3 = 14.282856857 Reorder the terms: 3 + x = 14.282856857 Solving 3 + x = 14.282856857 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 = 14.282856857 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.282856857 + -3 x = 14.282856857 + -3 Combine like terms: 14.282856857 + -3 = 11.282856857 x = 11.282856857 Simplifying x = 11.282856857Subproblem 2
x + 3 = -14.282856857 Simplifying x + 3 = -14.282856857 Reorder the terms: 3 + x = -14.282856857 Solving 3 + x = -14.282856857 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 = -14.282856857 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.282856857 + -3 x = -14.282856857 + -3 Combine like terms: -14.282856857 + -3 = -17.282856857 x = -17.282856857 Simplifying x = -17.282856857Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.282856857, -17.282856857}
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