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Simplifying x2 + -38x + -64 = 0 Reorder the terms: -64 + -38x + x2 = 0 Solving -64 + -38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -38x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -38x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -38x + x2 = 0 + 64 -38x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -38x + x2 = 64 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 = 64 + 361 Reorder the terms: 361 + -38x + x2 = 64 + 361 Combine like terms: 64 + 361 = 425 361 + -38x + x2 = 425 Factor a perfect square on the left side: (x + -19)(x + -19) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (x + -19) equal to 20.615528128 and -20.615528128.Subproblem 1
x + -19 = 20.615528128 Simplifying x + -19 = 20.615528128 Reorder the terms: -19 + x = 20.615528128 Solving -19 + x = 20.615528128 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 = 20.615528128 + 19 Combine like terms: -19 + 19 = 0 0 + x = 20.615528128 + 19 x = 20.615528128 + 19 Combine like terms: 20.615528128 + 19 = 39.615528128 x = 39.615528128 Simplifying x = 39.615528128Subproblem 2
x + -19 = -20.615528128 Simplifying x + -19 = -20.615528128 Reorder the terms: -19 + x = -20.615528128 Solving -19 + x = -20.615528128 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 = -20.615528128 + 19 Combine like terms: -19 + 19 = 0 0 + x = -20.615528128 + 19 x = -20.615528128 + 19 Combine like terms: -20.615528128 + 19 = -1.615528128 x = -1.615528128 Simplifying x = -1.615528128Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.615528128, -1.615528128}
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