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Simplifying x2 + -40x + -4 = 0 Reorder the terms: -4 + -40x + x2 = 0 Solving -4 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -40x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -40x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -40x + x2 = 0 + 4 -40x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -40x + x2 = 4 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 = 4 + 400 Reorder the terms: 400 + -40x + x2 = 4 + 400 Combine like terms: 4 + 400 = 404 400 + -40x + x2 = 404 Factor a perfect square on the left side: (x + -20)(x + -20) = 404 Calculate the square root of the right side: 20.099751242 Break this problem into two subproblems by setting (x + -20) equal to 20.099751242 and -20.099751242.Subproblem 1
x + -20 = 20.099751242 Simplifying x + -20 = 20.099751242 Reorder the terms: -20 + x = 20.099751242 Solving -20 + x = 20.099751242 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 = 20.099751242 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.099751242 + 20 x = 20.099751242 + 20 Combine like terms: 20.099751242 + 20 = 40.099751242 x = 40.099751242 Simplifying x = 40.099751242Subproblem 2
x + -20 = -20.099751242 Simplifying x + -20 = -20.099751242 Reorder the terms: -20 + x = -20.099751242 Solving -20 + x = -20.099751242 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 = -20.099751242 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.099751242 + 20 x = -20.099751242 + 20 Combine like terms: -20.099751242 + 20 = -0.099751242 x = -0.099751242 Simplifying x = -0.099751242Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.099751242, -0.099751242}
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