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Simplifying 40x + x2 = 4900 Solving 40x + x2 = 4900 Solving for variable 'x'. Reorder the terms: -4900 + 40x + x2 = 4900 + -4900 Combine like terms: 4900 + -4900 = 0 -4900 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4900' to each side of the equation. -4900 + 40x + 4900 + x2 = 0 + 4900 Reorder the terms: -4900 + 4900 + 40x + x2 = 0 + 4900 Combine like terms: -4900 + 4900 = 0 0 + 40x + x2 = 0 + 4900 40x + x2 = 0 + 4900 Combine like terms: 0 + 4900 = 4900 40x + x2 = 4900 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 = 4900 + 400 Reorder the terms: 400 + 40x + x2 = 4900 + 400 Combine like terms: 4900 + 400 = 5300 400 + 40x + x2 = 5300 Factor a perfect square on the left side: (x + 20)(x + 20) = 5300 Calculate the square root of the right side: 72.801098893 Break this problem into two subproblems by setting (x + 20) equal to 72.801098893 and -72.801098893.Subproblem 1
x + 20 = 72.801098893 Simplifying x + 20 = 72.801098893 Reorder the terms: 20 + x = 72.801098893 Solving 20 + x = 72.801098893 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 = 72.801098893 + -20 Combine like terms: 20 + -20 = 0 0 + x = 72.801098893 + -20 x = 72.801098893 + -20 Combine like terms: 72.801098893 + -20 = 52.801098893 x = 52.801098893 Simplifying x = 52.801098893Subproblem 2
x + 20 = -72.801098893 Simplifying x + 20 = -72.801098893 Reorder the terms: 20 + x = -72.801098893 Solving 20 + x = -72.801098893 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 = -72.801098893 + -20 Combine like terms: 20 + -20 = 0 0 + x = -72.801098893 + -20 x = -72.801098893 + -20 Combine like terms: -72.801098893 + -20 = -92.801098893 x = -92.801098893 Simplifying x = -92.801098893Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.801098893, -92.801098893}
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