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Simplifying x2 + 36x = 720 Reorder the terms: 36x + x2 = 720 Solving 36x + x2 = 720 Solving for variable 'x'. Reorder the terms: -720 + 36x + x2 = 720 + -720 Combine like terms: 720 + -720 = 0 -720 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '720' to each side of the equation. -720 + 36x + 720 + x2 = 0 + 720 Reorder the terms: -720 + 720 + 36x + x2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + 36x + x2 = 0 + 720 36x + x2 = 0 + 720 Combine like terms: 0 + 720 = 720 36x + x2 = 720 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 = 720 + 324 Reorder the terms: 324 + 36x + x2 = 720 + 324 Combine like terms: 720 + 324 = 1044 324 + 36x + x2 = 1044 Factor a perfect square on the left side: (x + 18)(x + 18) = 1044 Calculate the square root of the right side: 32.310988843 Break this problem into two subproblems by setting (x + 18) equal to 32.310988843 and -32.310988843.Subproblem 1
x + 18 = 32.310988843 Simplifying x + 18 = 32.310988843 Reorder the terms: 18 + x = 32.310988843 Solving 18 + x = 32.310988843 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 = 32.310988843 + -18 Combine like terms: 18 + -18 = 0 0 + x = 32.310988843 + -18 x = 32.310988843 + -18 Combine like terms: 32.310988843 + -18 = 14.310988843 x = 14.310988843 Simplifying x = 14.310988843Subproblem 2
x + 18 = -32.310988843 Simplifying x + 18 = -32.310988843 Reorder the terms: 18 + x = -32.310988843 Solving 18 + x = -32.310988843 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 = -32.310988843 + -18 Combine like terms: 18 + -18 = 0 0 + x = -32.310988843 + -18 x = -32.310988843 + -18 Combine like terms: -32.310988843 + -18 = -50.310988843 x = -50.310988843 Simplifying x = -50.310988843Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.310988843, -50.310988843}
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