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Simplifying x2 + -160x + 800 = 0 Reorder the terms: 800 + -160x + x2 = 0 Solving 800 + -160x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-800' to each side of the equation. 800 + -160x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -160x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -160x + x2 = 0 + -800 -160x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -160x + x2 = -800 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = -800 + 6400 Reorder the terms: 6400 + -160x + x2 = -800 + 6400 Combine like terms: -800 + 6400 = 5600 6400 + -160x + x2 = 5600 Factor a perfect square on the left side: (x + -80)(x + -80) = 5600 Calculate the square root of the right side: 74.833147735 Break this problem into two subproblems by setting (x + -80) equal to 74.833147735 and -74.833147735.Subproblem 1
x + -80 = 74.833147735 Simplifying x + -80 = 74.833147735 Reorder the terms: -80 + x = 74.833147735 Solving -80 + x = 74.833147735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 74.833147735 + 80 Combine like terms: -80 + 80 = 0 0 + x = 74.833147735 + 80 x = 74.833147735 + 80 Combine like terms: 74.833147735 + 80 = 154.833147735 x = 154.833147735 Simplifying x = 154.833147735Subproblem 2
x + -80 = -74.833147735 Simplifying x + -80 = -74.833147735 Reorder the terms: -80 + x = -74.833147735 Solving -80 + x = -74.833147735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -74.833147735 + 80 Combine like terms: -80 + 80 = 0 0 + x = -74.833147735 + 80 x = -74.833147735 + 80 Combine like terms: -74.833147735 + 80 = 5.166852265 x = 5.166852265 Simplifying x = 5.166852265Solution
The solution to the problem is based on the solutions from the subproblems. x = {154.833147735, 5.166852265}
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