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Simplifying x2 + -64x + -196 = 0 Reorder the terms: -196 + -64x + x2 = 0 Solving -196 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + -64x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + -64x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + -64x + x2 = 0 + 196 -64x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 -64x + x2 = 196 The x term is -64x. Take half its coefficient (-32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. -64x + 1024 + x2 = 196 + 1024 Reorder the terms: 1024 + -64x + x2 = 196 + 1024 Combine like terms: 196 + 1024 = 1220 1024 + -64x + x2 = 1220 Factor a perfect square on the left side: (x + -32)(x + -32) = 1220 Calculate the square root of the right side: 34.928498393 Break this problem into two subproblems by setting (x + -32) equal to 34.928498393 and -34.928498393.Subproblem 1
x + -32 = 34.928498393 Simplifying x + -32 = 34.928498393 Reorder the terms: -32 + x = 34.928498393 Solving -32 + x = 34.928498393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = 34.928498393 + 32 Combine like terms: -32 + 32 = 0 0 + x = 34.928498393 + 32 x = 34.928498393 + 32 Combine like terms: 34.928498393 + 32 = 66.928498393 x = 66.928498393 Simplifying x = 66.928498393Subproblem 2
x + -32 = -34.928498393 Simplifying x + -32 = -34.928498393 Reorder the terms: -32 + x = -34.928498393 Solving -32 + x = -34.928498393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = -34.928498393 + 32 Combine like terms: -32 + 32 = 0 0 + x = -34.928498393 + 32 x = -34.928498393 + 32 Combine like terms: -34.928498393 + 32 = -2.928498393 x = -2.928498393 Simplifying x = -2.928498393Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.928498393, -2.928498393}
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