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Simplifying x2 + -16x + -64 = 4x + 16 Reorder the terms: -64 + -16x + x2 = 4x + 16 Reorder the terms: -64 + -16x + x2 = 16 + 4x Solving -64 + -16x + x2 = 16 + 4x Solving for variable 'x'. Reorder the terms: -64 + -16 + -16x + -4x + x2 = 16 + 4x + -16 + -4x Combine like terms: -64 + -16 = -80 -80 + -16x + -4x + x2 = 16 + 4x + -16 + -4x Combine like terms: -16x + -4x = -20x -80 + -20x + x2 = 16 + 4x + -16 + -4x Reorder the terms: -80 + -20x + x2 = 16 + -16 + 4x + -4x Combine like terms: 16 + -16 = 0 -80 + -20x + x2 = 0 + 4x + -4x -80 + -20x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -80 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -20x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -20x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -20x + x2 = 0 + 80 -20x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -20x + x2 = 80 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 80 + 100 Reorder the terms: 100 + -20x + x2 = 80 + 100 Combine like terms: 80 + 100 = 180 100 + -20x + x2 = 180 Factor a perfect square on the left side: (x + -10)(x + -10) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -10) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -10 = 13.416407865 Simplifying x + -10 = 13.416407865 Reorder the terms: -10 + x = 13.416407865 Solving -10 + x = 13.416407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 13.416407865 + 10 Combine like terms: -10 + 10 = 0 0 + x = 13.416407865 + 10 x = 13.416407865 + 10 Combine like terms: 13.416407865 + 10 = 23.416407865 x = 23.416407865 Simplifying x = 23.416407865Subproblem 2
x + -10 = -13.416407865 Simplifying x + -10 = -13.416407865 Reorder the terms: -10 + x = -13.416407865 Solving -10 + x = -13.416407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -13.416407865 + 10 Combine like terms: -10 + 10 = 0 0 + x = -13.416407865 + 10 x = -13.416407865 + 10 Combine like terms: -13.416407865 + 10 = -3.416407865 x = -3.416407865 Simplifying x = -3.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.416407865, -3.416407865}
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