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Simplifying 20x2 + 21x + -60 = 0 Reorder the terms: -60 + 21x + 20x2 = 0 Solving -60 + 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'. -3 + 1.05x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.05x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.05x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.05x + x2 = 0 + 3 1.05x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.05x + x2 = 3 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 = 3 + 0.275625 Reorder the terms: 0.275625 + 1.05x + x2 = 3 + 0.275625 Combine like terms: 3 + 0.275625 = 3.275625 0.275625 + 1.05x + x2 = 3.275625 Factor a perfect square on the left side: (x + 0.525)(x + 0.525) = 3.275625 Calculate the square root of the right side: 1.80986878 Break this problem into two subproblems by setting (x + 0.525) equal to 1.80986878 and -1.80986878.Subproblem 1
x + 0.525 = 1.80986878 Simplifying x + 0.525 = 1.80986878 Reorder the terms: 0.525 + x = 1.80986878 Solving 0.525 + x = 1.80986878 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 = 1.80986878 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = 1.80986878 + -0.525 x = 1.80986878 + -0.525 Combine like terms: 1.80986878 + -0.525 = 1.28486878 x = 1.28486878 Simplifying x = 1.28486878Subproblem 2
x + 0.525 = -1.80986878 Simplifying x + 0.525 = -1.80986878 Reorder the terms: 0.525 + x = -1.80986878 Solving 0.525 + x = -1.80986878 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 = -1.80986878 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = -1.80986878 + -0.525 x = -1.80986878 + -0.525 Combine like terms: -1.80986878 + -0.525 = -2.33486878 x = -2.33486878 Simplifying x = -2.33486878Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.28486878, -2.33486878}
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