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Simplifying (x + 40)(x + -40) = 180x Reorder the terms: (40 + x)(x + -40) = 180x Reorder the terms: (40 + x)(-40 + x) = 180x Multiply (40 + x) * (-40 + x) (40(-40 + x) + x(-40 + x)) = 180x ((-40 * 40 + x * 40) + x(-40 + x)) = 180x ((-1600 + 40x) + x(-40 + x)) = 180x (-1600 + 40x + (-40 * x + x * x)) = 180x (-1600 + 40x + (-40x + x2)) = 180x Combine like terms: 40x + -40x = 0 (-1600 + 0 + x2) = 180x (-1600 + x2) = 180x Solving -1600 + x2 = 180x Solving for variable 'x'. Reorder the terms: -1600 + -180x + x2 = 180x + -180x Combine like terms: 180x + -180x = 0 -1600 + -180x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1600' to each side of the equation. -1600 + -180x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + -180x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + -180x + x2 = 0 + 1600 -180x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 -180x + x2 = 1600 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = 1600 + 8100 Reorder the terms: 8100 + -180x + x2 = 1600 + 8100 Combine like terms: 1600 + 8100 = 9700 8100 + -180x + x2 = 9700 Factor a perfect square on the left side: (x + -90)(x + -90) = 9700 Calculate the square root of the right side: 98.488578018 Break this problem into two subproblems by setting (x + -90) equal to 98.488578018 and -98.488578018.Subproblem 1
x + -90 = 98.488578018 Simplifying x + -90 = 98.488578018 Reorder the terms: -90 + x = 98.488578018 Solving -90 + x = 98.488578018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 98.488578018 + 90 Combine like terms: -90 + 90 = 0 0 + x = 98.488578018 + 90 x = 98.488578018 + 90 Combine like terms: 98.488578018 + 90 = 188.488578018 x = 188.488578018 Simplifying x = 188.488578018Subproblem 2
x + -90 = -98.488578018 Simplifying x + -90 = -98.488578018 Reorder the terms: -90 + x = -98.488578018 Solving -90 + x = -98.488578018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -98.488578018 + 90 Combine like terms: -90 + 90 = 0 0 + x = -98.488578018 + 90 x = -98.488578018 + 90 Combine like terms: -98.488578018 + 90 = -8.488578018 x = -8.488578018 Simplifying x = -8.488578018Solution
The solution to the problem is based on the solutions from the subproblems. x = {188.488578018, -8.488578018}
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