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Simplifying x2 + -2x + -324 = 2x Reorder the terms: -324 + -2x + x2 = 2x Solving -324 + -2x + x2 = 2x Solving for variable 'x'. Reorder the terms: -324 + -2x + -2x + x2 = 2x + -2x Combine like terms: -2x + -2x = -4x -324 + -4x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -324 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + -4x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + -4x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + -4x + x2 = 0 + 324 -4x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 -4x + x2 = 324 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 324 + 4 Reorder the terms: 4 + -4x + x2 = 324 + 4 Combine like terms: 324 + 4 = 328 4 + -4x + x2 = 328 Factor a perfect square on the left side: (x + -2)(x + -2) = 328 Calculate the square root of the right side: 18.110770276 Break this problem into two subproblems by setting (x + -2) equal to 18.110770276 and -18.110770276.Subproblem 1
x + -2 = 18.110770276 Simplifying x + -2 = 18.110770276 Reorder the terms: -2 + x = 18.110770276 Solving -2 + x = 18.110770276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 18.110770276 + 2 Combine like terms: -2 + 2 = 0 0 + x = 18.110770276 + 2 x = 18.110770276 + 2 Combine like terms: 18.110770276 + 2 = 20.110770276 x = 20.110770276 Simplifying x = 20.110770276Subproblem 2
x + -2 = -18.110770276 Simplifying x + -2 = -18.110770276 Reorder the terms: -2 + x = -18.110770276 Solving -2 + x = -18.110770276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -18.110770276 + 2 Combine like terms: -2 + 2 = 0 0 + x = -18.110770276 + 2 x = -18.110770276 + 2 Combine like terms: -18.110770276 + 2 = -16.110770276 x = -16.110770276 Simplifying x = -16.110770276Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.110770276, -16.110770276}
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