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Simplifying x2 + -4x = 4050 Reorder the terms: -4x + x2 = 4050 Solving -4x + x2 = 4050 Solving for variable 'x'. Reorder the terms: -4050 + -4x + x2 = 4050 + -4050 Combine like terms: 4050 + -4050 = 0 -4050 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4050' to each side of the equation. -4050 + -4x + 4050 + x2 = 0 + 4050 Reorder the terms: -4050 + 4050 + -4x + x2 = 0 + 4050 Combine like terms: -4050 + 4050 = 0 0 + -4x + x2 = 0 + 4050 -4x + x2 = 0 + 4050 Combine like terms: 0 + 4050 = 4050 -4x + x2 = 4050 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 4050 + 4 Reorder the terms: 4 + -4x + x2 = 4050 + 4 Combine like terms: 4050 + 4 = 4054 4 + -4x + x2 = 4054 Factor a perfect square on the left side: (x + -2)(x + -2) = 4054 Calculate the square root of the right side: 63.671029519 Break this problem into two subproblems by setting (x + -2) equal to 63.671029519 and -63.671029519.Subproblem 1
x + -2 = 63.671029519 Simplifying x + -2 = 63.671029519 Reorder the terms: -2 + x = 63.671029519 Solving -2 + x = 63.671029519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 63.671029519 + 2 Combine like terms: -2 + 2 = 0 0 + x = 63.671029519 + 2 x = 63.671029519 + 2 Combine like terms: 63.671029519 + 2 = 65.671029519 x = 65.671029519 Simplifying x = 65.671029519Subproblem 2
x + -2 = -63.671029519 Simplifying x + -2 = -63.671029519 Reorder the terms: -2 + x = -63.671029519 Solving -2 + x = -63.671029519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -63.671029519 + 2 Combine like terms: -2 + 2 = 0 0 + x = -63.671029519 + 2 x = -63.671029519 + 2 Combine like terms: -63.671029519 + 2 = -61.671029519 x = -61.671029519 Simplifying x = -61.671029519Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.671029519, -61.671029519}
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