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Simplifying x2 + -80x + -2 = 0 Reorder the terms: -2 + -80x + x2 = 0 Solving -2 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -80x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -80x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -80x + x2 = 0 + 2 -80x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -80x + x2 = 2 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 = 2 + 1600 Reorder the terms: 1600 + -80x + x2 = 2 + 1600 Combine like terms: 2 + 1600 = 1602 1600 + -80x + x2 = 1602 Factor a perfect square on the left side: (x + -40)(x + -40) = 1602 Calculate the square root of the right side: 40.024992192 Break this problem into two subproblems by setting (x + -40) equal to 40.024992192 and -40.024992192.Subproblem 1
x + -40 = 40.024992192 Simplifying x + -40 = 40.024992192 Reorder the terms: -40 + x = 40.024992192 Solving -40 + x = 40.024992192 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 = 40.024992192 + 40 Combine like terms: -40 + 40 = 0 0 + x = 40.024992192 + 40 x = 40.024992192 + 40 Combine like terms: 40.024992192 + 40 = 80.024992192 x = 80.024992192 Simplifying x = 80.024992192Subproblem 2
x + -40 = -40.024992192 Simplifying x + -40 = -40.024992192 Reorder the terms: -40 + x = -40.024992192 Solving -40 + x = -40.024992192 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 = -40.024992192 + 40 Combine like terms: -40 + 40 = 0 0 + x = -40.024992192 + 40 x = -40.024992192 + 40 Combine like terms: -40.024992192 + 40 = -0.024992192 x = -0.024992192 Simplifying x = -0.024992192Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.024992192, -0.024992192}
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