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Simplifying 2x2 + -160x + 275 = 0 Reorder the terms: 275 + -160x + 2x2 = 0 Solving 275 + -160x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 137.5 + -80x + x2 = 0 Move the constant term to the right: Add '-137.5' to each side of the equation. 137.5 + -80x + -137.5 + x2 = 0 + -137.5 Reorder the terms: 137.5 + -137.5 + -80x + x2 = 0 + -137.5 Combine like terms: 137.5 + -137.5 = 0.0 0.0 + -80x + x2 = 0 + -137.5 -80x + x2 = 0 + -137.5 Combine like terms: 0 + -137.5 = -137.5 -80x + x2 = -137.5 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 = -137.5 + 1600 Reorder the terms: 1600 + -80x + x2 = -137.5 + 1600 Combine like terms: -137.5 + 1600 = 1462.5 1600 + -80x + x2 = 1462.5 Factor a perfect square on the left side: (x + -40)(x + -40) = 1462.5 Calculate the square root of the right side: 38.242646352 Break this problem into two subproblems by setting (x + -40) equal to 38.242646352 and -38.242646352.Subproblem 1
x + -40 = 38.242646352 Simplifying x + -40 = 38.242646352 Reorder the terms: -40 + x = 38.242646352 Solving -40 + x = 38.242646352 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 = 38.242646352 + 40 Combine like terms: -40 + 40 = 0 0 + x = 38.242646352 + 40 x = 38.242646352 + 40 Combine like terms: 38.242646352 + 40 = 78.242646352 x = 78.242646352 Simplifying x = 78.242646352Subproblem 2
x + -40 = -38.242646352 Simplifying x + -40 = -38.242646352 Reorder the terms: -40 + x = -38.242646352 Solving -40 + x = -38.242646352 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 = -38.242646352 + 40 Combine like terms: -40 + 40 = 0 0 + x = -38.242646352 + 40 x = -38.242646352 + 40 Combine like terms: -38.242646352 + 40 = 1.757353648 x = 1.757353648 Simplifying x = 1.757353648Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.242646352, 1.757353648}
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