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Simplifying x2 + -80x = 36 Reorder the terms: -80x + x2 = 36 Solving -80x + x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + -80x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -80x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -80x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -80x + x2 = 0 + 36 -80x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -80x + x2 = 36 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 = 36 + 1600 Reorder the terms: 1600 + -80x + x2 = 36 + 1600 Combine like terms: 36 + 1600 = 1636 1600 + -80x + x2 = 1636 Factor a perfect square on the left side: (x + -40)(x + -40) = 1636 Calculate the square root of the right side: 40.447496832 Break this problem into two subproblems by setting (x + -40) equal to 40.447496832 and -40.447496832.Subproblem 1
x + -40 = 40.447496832 Simplifying x + -40 = 40.447496832 Reorder the terms: -40 + x = 40.447496832 Solving -40 + x = 40.447496832 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 = 40.447496832 + 40 Combine like terms: -40 + 40 = 0 0 + x = 40.447496832 + 40 x = 40.447496832 + 40 Combine like terms: 40.447496832 + 40 = 80.447496832 x = 80.447496832 Simplifying x = 80.447496832Subproblem 2
x + -40 = -40.447496832 Simplifying x + -40 = -40.447496832 Reorder the terms: -40 + x = -40.447496832 Solving -40 + x = -40.447496832 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 = -40.447496832 + 40 Combine like terms: -40 + 40 = 0 0 + x = -40.447496832 + 40 x = -40.447496832 + 40 Combine like terms: -40.447496832 + 40 = -0.447496832 x = -0.447496832 Simplifying x = -0.447496832Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.447496832, -0.447496832}
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