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Simplifying x2 + -40x = 383 Reorder the terms: -40x + x2 = 383 Solving -40x + x2 = 383 Solving for variable 'x'. Reorder the terms: -383 + -40x + x2 = 383 + -383 Combine like terms: 383 + -383 = 0 -383 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '383' to each side of the equation. -383 + -40x + 383 + x2 = 0 + 383 Reorder the terms: -383 + 383 + -40x + x2 = 0 + 383 Combine like terms: -383 + 383 = 0 0 + -40x + x2 = 0 + 383 -40x + x2 = 0 + 383 Combine like terms: 0 + 383 = 383 -40x + x2 = 383 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 = 383 + 400 Reorder the terms: 400 + -40x + x2 = 383 + 400 Combine like terms: 383 + 400 = 783 400 + -40x + x2 = 783 Factor a perfect square on the left side: (x + -20)(x + -20) = 783 Calculate the square root of the right side: 27.982137159 Break this problem into two subproblems by setting (x + -20) equal to 27.982137159 and -27.982137159.Subproblem 1
x + -20 = 27.982137159 Simplifying x + -20 = 27.982137159 Reorder the terms: -20 + x = 27.982137159 Solving -20 + x = 27.982137159 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 = 27.982137159 + 20 Combine like terms: -20 + 20 = 0 0 + x = 27.982137159 + 20 x = 27.982137159 + 20 Combine like terms: 27.982137159 + 20 = 47.982137159 x = 47.982137159 Simplifying x = 47.982137159Subproblem 2
x + -20 = -27.982137159 Simplifying x + -20 = -27.982137159 Reorder the terms: -20 + x = -27.982137159 Solving -20 + x = -27.982137159 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 = -27.982137159 + 20 Combine like terms: -20 + 20 = 0 0 + x = -27.982137159 + 20 x = -27.982137159 + 20 Combine like terms: -27.982137159 + 20 = -7.982137159 x = -7.982137159 Simplifying x = -7.982137159Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.982137159, -7.982137159}
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