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Simplifying x2 + -36x + 300 = 0 Reorder the terms: 300 + -36x + x2 = 0 Solving 300 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-300' to each side of the equation. 300 + -36x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -36x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -36x + x2 = 0 + -300 -36x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -36x + x2 = -300 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 = -300 + 324 Reorder the terms: 324 + -36x + x2 = -300 + 324 Combine like terms: -300 + 324 = 24 324 + -36x + x2 = 24 Factor a perfect square on the left side: (x + -18)(x + -18) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -18) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -18 = 4.898979486 Simplifying x + -18 = 4.898979486 Reorder the terms: -18 + x = 4.898979486 Solving -18 + x = 4.898979486 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 = 4.898979486 + 18 Combine like terms: -18 + 18 = 0 0 + x = 4.898979486 + 18 x = 4.898979486 + 18 Combine like terms: 4.898979486 + 18 = 22.898979486 x = 22.898979486 Simplifying x = 22.898979486Subproblem 2
x + -18 = -4.898979486 Simplifying x + -18 = -4.898979486 Reorder the terms: -18 + x = -4.898979486 Solving -18 + x = -4.898979486 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 = -4.898979486 + 18 Combine like terms: -18 + 18 = 0 0 + x = -4.898979486 + 18 x = -4.898979486 + 18 Combine like terms: -4.898979486 + 18 = 13.101020514 x = 13.101020514 Simplifying x = 13.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.898979486, 13.101020514}
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