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Simplifying 21 = 40x + -1x2 Solving 21 = 40x + -1x2 Solving for variable 'x'. Reorder the terms: 21 + -40x + x2 = 40x + -40x + -1x2 + x2 Combine like terms: 40x + -40x = 0 21 + -40x + x2 = 0 + -1x2 + x2 21 + -40x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 21 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -40x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -40x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -40x + x2 = 0 + -21 -40x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -40x + x2 = -21 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -21 + 400 Reorder the terms: 400 + -40x + x2 = -21 + 400 Combine like terms: -21 + 400 = 379 400 + -40x + x2 = 379 Factor a perfect square on the left side: (x + -20)(x + -20) = 379 Calculate the square root of the right side: 19.467922334 Break this problem into two subproblems by setting (x + -20) equal to 19.467922334 and -19.467922334.Subproblem 1
x + -20 = 19.467922334 Simplifying x + -20 = 19.467922334 Reorder the terms: -20 + x = 19.467922334 Solving -20 + x = 19.467922334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.467922334 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.467922334 + 20 x = 19.467922334 + 20 Combine like terms: 19.467922334 + 20 = 39.467922334 x = 39.467922334 Simplifying x = 39.467922334Subproblem 2
x + -20 = -19.467922334 Simplifying x + -20 = -19.467922334 Reorder the terms: -20 + x = -19.467922334 Solving -20 + x = -19.467922334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.467922334 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.467922334 + 20 x = -19.467922334 + 20 Combine like terms: -19.467922334 + 20 = 0.532077666 x = 0.532077666 Simplifying x = 0.532077666Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.467922334, 0.532077666}
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