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Simplifying x2 + 36x + 324 = 10 Reorder the terms: 324 + 36x + x2 = 10 Solving 324 + 36x + x2 = 10 Solving for variable 'x'. Reorder the terms: 324 + -10 + 36x + x2 = 10 + -10 Combine like terms: 324 + -10 = 314 314 + 36x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 314 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-314' to each side of the equation. 314 + 36x + -314 + x2 = 0 + -314 Reorder the terms: 314 + -314 + 36x + x2 = 0 + -314 Combine like terms: 314 + -314 = 0 0 + 36x + x2 = 0 + -314 36x + x2 = 0 + -314 Combine like terms: 0 + -314 = -314 36x + x2 = -314 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -314 + 324 Reorder the terms: 324 + 36x + x2 = -314 + 324 Combine like terms: -314 + 324 = 10 324 + 36x + x2 = 10 Factor a perfect square on the left side: (x + 18)(x + 18) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 18) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 18 = 3.16227766 Simplifying x + 18 = 3.16227766 Reorder the terms: 18 + x = 3.16227766 Solving 18 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 3.16227766 + -18 Combine like terms: 18 + -18 = 0 0 + x = 3.16227766 + -18 x = 3.16227766 + -18 Combine like terms: 3.16227766 + -18 = -14.83772234 x = -14.83772234 Simplifying x = -14.83772234Subproblem 2
x + 18 = -3.16227766 Simplifying x + 18 = -3.16227766 Reorder the terms: 18 + x = -3.16227766 Solving 18 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -3.16227766 + -18 Combine like terms: 18 + -18 = 0 0 + x = -3.16227766 + -18 x = -3.16227766 + -18 Combine like terms: -3.16227766 + -18 = -21.16227766 x = -21.16227766 Simplifying x = -21.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-14.83772234, -21.16227766}
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