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Simplifying x2 + -4x = 350 Reorder the terms: -4x + x2 = 350 Solving -4x + x2 = 350 Solving for variable 'x'. Reorder the terms: -350 + -4x + x2 = 350 + -350 Combine like terms: 350 + -350 = 0 -350 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + -4x + 350 + x2 = 0 + 350 Reorder the terms: -350 + 350 + -4x + x2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + -4x + x2 = 0 + 350 -4x + x2 = 0 + 350 Combine like terms: 0 + 350 = 350 -4x + x2 = 350 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 = 350 + 4 Reorder the terms: 4 + -4x + x2 = 350 + 4 Combine like terms: 350 + 4 = 354 4 + -4x + x2 = 354 Factor a perfect square on the left side: (x + -2)(x + -2) = 354 Calculate the square root of the right side: 18.814887722 Break this problem into two subproblems by setting (x + -2) equal to 18.814887722 and -18.814887722.Subproblem 1
x + -2 = 18.814887722 Simplifying x + -2 = 18.814887722 Reorder the terms: -2 + x = 18.814887722 Solving -2 + x = 18.814887722 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 = 18.814887722 + 2 Combine like terms: -2 + 2 = 0 0 + x = 18.814887722 + 2 x = 18.814887722 + 2 Combine like terms: 18.814887722 + 2 = 20.814887722 x = 20.814887722 Simplifying x = 20.814887722Subproblem 2
x + -2 = -18.814887722 Simplifying x + -2 = -18.814887722 Reorder the terms: -2 + x = -18.814887722 Solving -2 + x = -18.814887722 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 = -18.814887722 + 2 Combine like terms: -2 + 2 = 0 0 + x = -18.814887722 + 2 x = -18.814887722 + 2 Combine like terms: -18.814887722 + 2 = -16.814887722 x = -16.814887722 Simplifying x = -16.814887722Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.814887722, -16.814887722}
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