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Simplifying 20x2 + -21x + -500 = 0 Reorder the terms: -500 + -21x + 20x2 = 0 Solving -500 + -21x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -25 + -1.05x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -1.05x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -1.05x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1.05x + x2 = 0 + 25 -1.05x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -1.05x + x2 = 25 The x term is -1.05x. Take half its coefficient (-0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. -1.05x + 0.275625 + x2 = 25 + 0.275625 Reorder the terms: 0.275625 + -1.05x + x2 = 25 + 0.275625 Combine like terms: 25 + 0.275625 = 25.275625 0.275625 + -1.05x + x2 = 25.275625 Factor a perfect square on the left side: (x + -0.525)(x + -0.525) = 25.275625 Calculate the square root of the right side: 5.027486947 Break this problem into two subproblems by setting (x + -0.525) equal to 5.027486947 and -5.027486947.Subproblem 1
x + -0.525 = 5.027486947 Simplifying x + -0.525 = 5.027486947 Reorder the terms: -0.525 + x = 5.027486947 Solving -0.525 + x = 5.027486947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + x = 5.027486947 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + x = 5.027486947 + 0.525 x = 5.027486947 + 0.525 Combine like terms: 5.027486947 + 0.525 = 5.552486947 x = 5.552486947 Simplifying x = 5.552486947Subproblem 2
x + -0.525 = -5.027486947 Simplifying x + -0.525 = -5.027486947 Reorder the terms: -0.525 + x = -5.027486947 Solving -0.525 + x = -5.027486947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + x = -5.027486947 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + x = -5.027486947 + 0.525 x = -5.027486947 + 0.525 Combine like terms: -5.027486947 + 0.525 = -4.502486947 x = -4.502486947 Simplifying x = -4.502486947Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.552486947, -4.502486947}
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