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Simplifying 0 = x2 + -4x + -35 Reorder the terms: 0 = -35 + -4x + x2 Solving 0 = -35 + -4x + x2 Solving for variable 'x'. Combine like terms: 0 + 35 = 35 35 + 4x + -1x2 = -35 + -4x + x2 + 35 + 4x + -1x2 Reorder the terms: 35 + 4x + -1x2 = -35 + 35 + -4x + 4x + x2 + -1x2 Combine like terms: -35 + 35 = 0 35 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2 35 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 35 + 4x + -1x2 = 0 + x2 + -1x2 35 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 35 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + -4x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -4x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -4x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -4x + x2 = 0 + 35 -4x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -4x + x2 = 35 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 = 35 + 4 Reorder the terms: 4 + -4x + x2 = 35 + 4 Combine like terms: 35 + 4 = 39 4 + -4x + x2 = 39 Factor a perfect square on the left side: (x + -2)(x + -2) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -2) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -2 = 6.244997998 Simplifying x + -2 = 6.244997998 Reorder the terms: -2 + x = 6.244997998 Solving -2 + x = 6.244997998 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 = 6.244997998 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.244997998 + 2 x = 6.244997998 + 2 Combine like terms: 6.244997998 + 2 = 8.244997998 x = 8.244997998 Simplifying x = 8.244997998Subproblem 2
x + -2 = -6.244997998 Simplifying x + -2 = -6.244997998 Reorder the terms: -2 + x = -6.244997998 Solving -2 + x = -6.244997998 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 = -6.244997998 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.244997998 + 2 x = -6.244997998 + 2 Combine like terms: -6.244997998 + 2 = -4.244997998 x = -4.244997998 Simplifying x = -4.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.244997998, -4.244997998}
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