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Simplifying 144 + x2 = 36x Solving 144 + x2 = 36x Solving for variable 'x'. Reorder the terms: 144 + -36x + x2 = 36x + -36x Combine like terms: 36x + -36x = 0 144 + -36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + -36x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + -36x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -36x + x2 = 0 + -144 -36x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 -36x + x2 = -144 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 = -144 + 324 Reorder the terms: 324 + -36x + x2 = -144 + 324 Combine like terms: -144 + 324 = 180 324 + -36x + x2 = 180 Factor a perfect square on the left side: (x + -18)(x + -18) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -18) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -18 = 13.416407865 Simplifying x + -18 = 13.416407865 Reorder the terms: -18 + x = 13.416407865 Solving -18 + x = 13.416407865 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 = 13.416407865 + 18 Combine like terms: -18 + 18 = 0 0 + x = 13.416407865 + 18 x = 13.416407865 + 18 Combine like terms: 13.416407865 + 18 = 31.416407865 x = 31.416407865 Simplifying x = 31.416407865Subproblem 2
x + -18 = -13.416407865 Simplifying x + -18 = -13.416407865 Reorder the terms: -18 + x = -13.416407865 Solving -18 + x = -13.416407865 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 = -13.416407865 + 18 Combine like terms: -18 + 18 = 0 0 + x = -13.416407865 + 18 x = -13.416407865 + 18 Combine like terms: -13.416407865 + 18 = 4.583592135 x = 4.583592135 Simplifying x = 4.583592135Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.416407865, 4.583592135}
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