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Simplifying X * X + 40X = 60 Multiply X * X X2 + 40X = 60 Reorder the terms: 40X + X2 = 60 Solving 40X + X2 = 60 Solving for variable 'X'. Reorder the terms: -60 + 40X + X2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 40X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 40X + 60 + X2 = 0 + 60 Reorder the terms: -60 + 60 + 40X + X2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 40X + X2 = 0 + 60 40X + X2 = 0 + 60 Combine like terms: 0 + 60 = 60 40X + X2 = 60 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 = 60 + 400 Reorder the terms: 400 + 40X + X2 = 60 + 400 Combine like terms: 60 + 400 = 460 400 + 40X + X2 = 460 Factor a perfect square on the left side: (X + 20)(X + 20) = 460 Calculate the square root of the right side: 21.44761059 Break this problem into two subproblems by setting (X + 20) equal to 21.44761059 and -21.44761059.Subproblem 1
X + 20 = 21.44761059 Simplifying X + 20 = 21.44761059 Reorder the terms: 20 + X = 21.44761059 Solving 20 + X = 21.44761059 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 = 21.44761059 + -20 Combine like terms: 20 + -20 = 0 0 + X = 21.44761059 + -20 X = 21.44761059 + -20 Combine like terms: 21.44761059 + -20 = 1.44761059 X = 1.44761059 Simplifying X = 1.44761059Subproblem 2
X + 20 = -21.44761059 Simplifying X + 20 = -21.44761059 Reorder the terms: 20 + X = -21.44761059 Solving 20 + X = -21.44761059 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 = -21.44761059 + -20 Combine like terms: 20 + -20 = 0 0 + X = -21.44761059 + -20 X = -21.44761059 + -20 Combine like terms: -21.44761059 + -20 = -41.44761059 X = -41.44761059 Simplifying X = -41.44761059Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.44761059, -41.44761059}
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