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Simplifying X2 + -40X + 3 = 0 Reorder the terms: 3 + -40X + X2 = 0 Solving 3 + -40X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -40X + -3 + X2 = 0 + -3 Reorder the terms: 3 + -3 + -40X + X2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -40X + X2 = 0 + -3 -40X + X2 = 0 + -3 Combine like terms: 0 + -3 = -3 -40X + X2 = -3 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 = -3 + 400 Reorder the terms: 400 + -40X + X2 = -3 + 400 Combine like terms: -3 + 400 = 397 400 + -40X + X2 = 397 Factor a perfect square on the left side: (X + -20)(X + -20) = 397 Calculate the square root of the right side: 19.924858845 Break this problem into two subproblems by setting (X + -20) equal to 19.924858845 and -19.924858845.Subproblem 1
X + -20 = 19.924858845 Simplifying X + -20 = 19.924858845 Reorder the terms: -20 + X = 19.924858845 Solving -20 + X = 19.924858845 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 = 19.924858845 + 20 Combine like terms: -20 + 20 = 0 0 + X = 19.924858845 + 20 X = 19.924858845 + 20 Combine like terms: 19.924858845 + 20 = 39.924858845 X = 39.924858845 Simplifying X = 39.924858845Subproblem 2
X + -20 = -19.924858845 Simplifying X + -20 = -19.924858845 Reorder the terms: -20 + X = -19.924858845 Solving -20 + X = -19.924858845 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 = -19.924858845 + 20 Combine like terms: -20 + 20 = 0 0 + X = -19.924858845 + 20 X = -19.924858845 + 20 Combine like terms: -19.924858845 + 20 = 0.075141155 X = 0.075141155 Simplifying X = 0.075141155Solution
The solution to the problem is based on the solutions from the subproblems. X = {39.924858845, 0.075141155}
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