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Simplifying x2 + -8x + -164 = 0 Reorder the terms: -164 + -8x + x2 = 0 Solving -164 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + -8x + 164 + x2 = 0 + 164 Reorder the terms: -164 + 164 + -8x + x2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + -8x + x2 = 0 + 164 -8x + x2 = 0 + 164 Combine like terms: 0 + 164 = 164 -8x + x2 = 164 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 164 + 16 Reorder the terms: 16 + -8x + x2 = 164 + 16 Combine like terms: 164 + 16 = 180 16 + -8x + x2 = 180 Factor a perfect square on the left side: (x + -4)(x + -4) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -4) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -4 = 13.416407865 Simplifying x + -4 = 13.416407865 Reorder the terms: -4 + x = 13.416407865 Solving -4 + x = 13.416407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 13.416407865 + 4 Combine like terms: -4 + 4 = 0 0 + x = 13.416407865 + 4 x = 13.416407865 + 4 Combine like terms: 13.416407865 + 4 = 17.416407865 x = 17.416407865 Simplifying x = 17.416407865Subproblem 2
x + -4 = -13.416407865 Simplifying x + -4 = -13.416407865 Reorder the terms: -4 + x = -13.416407865 Solving -4 + x = -13.416407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -13.416407865 + 4 Combine like terms: -4 + 4 = 0 0 + x = -13.416407865 + 4 x = -13.416407865 + 4 Combine like terms: -13.416407865 + 4 = -9.416407865 x = -9.416407865 Simplifying x = -9.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.416407865, -9.416407865}
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