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Simplifying x2 + -80x + -12 = 0 Reorder the terms: -12 + -80x + x2 = 0 Solving -12 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -80x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -80x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -80x + x2 = 0 + 12 -80x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -80x + x2 = 12 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 12 + 1600 Reorder the terms: 1600 + -80x + x2 = 12 + 1600 Combine like terms: 12 + 1600 = 1612 1600 + -80x + x2 = 1612 Factor a perfect square on the left side: (x + -40)(x + -40) = 1612 Calculate the square root of the right side: 40.1497198 Break this problem into two subproblems by setting (x + -40) equal to 40.1497198 and -40.1497198.Subproblem 1
x + -40 = 40.1497198 Simplifying x + -40 = 40.1497198 Reorder the terms: -40 + x = 40.1497198 Solving -40 + x = 40.1497198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 40.1497198 + 40 Combine like terms: -40 + 40 = 0 0 + x = 40.1497198 + 40 x = 40.1497198 + 40 Combine like terms: 40.1497198 + 40 = 80.1497198 x = 80.1497198 Simplifying x = 80.1497198Subproblem 2
x + -40 = -40.1497198 Simplifying x + -40 = -40.1497198 Reorder the terms: -40 + x = -40.1497198 Solving -40 + x = -40.1497198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -40.1497198 + 40 Combine like terms: -40 + 40 = 0 0 + x = -40.1497198 + 40 x = -40.1497198 + 40 Combine like terms: -40.1497198 + 40 = -0.1497198 x = -0.1497198 Simplifying x = -0.1497198Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.1497198, -0.1497198}
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