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Simplifying x2 + -36x + 324 + x2 + -2x + -1 = x2 Reorder the terms: 324 + -1 + -36x + -2x + x2 + x2 = x2 Combine like terms: 324 + -1 = 323 323 + -36x + -2x + x2 + x2 = x2 Combine like terms: -36x + -2x = -38x 323 + -38x + x2 + x2 = x2 Combine like terms: x2 + x2 = 2x2 323 + -38x + 2x2 = x2 Solving 323 + -38x + 2x2 = x2 Solving for variable 'x'. Combine like terms: 2x2 + -1x2 = 1x2 323 + -38x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 323 + -38x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-323' to each side of the equation. 323 + -38x + -323 + x2 = 0 + -323 Reorder the terms: 323 + -323 + -38x + x2 = 0 + -323 Combine like terms: 323 + -323 = 0 0 + -38x + x2 = 0 + -323 -38x + x2 = 0 + -323 Combine like terms: 0 + -323 = -323 -38x + x2 = -323 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = -323 + 361 Reorder the terms: 361 + -38x + x2 = -323 + 361 Combine like terms: -323 + 361 = 38 361 + -38x + x2 = 38 Factor a perfect square on the left side: (x + -19)(x + -19) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + -19) equal to 6.164414003 and -6.164414003.Subproblem 1
x + -19 = 6.164414003 Simplifying x + -19 = 6.164414003 Reorder the terms: -19 + x = 6.164414003 Solving -19 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 6.164414003 + 19 Combine like terms: -19 + 19 = 0 0 + x = 6.164414003 + 19 x = 6.164414003 + 19 Combine like terms: 6.164414003 + 19 = 25.164414003 x = 25.164414003 Simplifying x = 25.164414003Subproblem 2
x + -19 = -6.164414003 Simplifying x + -19 = -6.164414003 Reorder the terms: -19 + x = -6.164414003 Solving -19 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -6.164414003 + 19 Combine like terms: -19 + 19 = 0 0 + x = -6.164414003 + 19 x = -6.164414003 + 19 Combine like terms: -6.164414003 + 19 = 12.835585997 x = 12.835585997 Simplifying x = 12.835585997Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.164414003, 12.835585997}
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