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Simplifying x2 + -35 = 7x Reorder the terms: -35 + x2 = 7x Solving -35 + x2 = 7x Solving for variable 'x'. Reorder the terms: -35 + -7x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -35 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -7x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -7x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -7x + x2 = 0 + 35 -7x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -7x + x2 = 35 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 35 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 35 + 12.25 Combine like terms: 35 + 12.25 = 47.25 12.25 + -7x + x2 = 47.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + -3.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + -3.5 = 6.873863542 Simplifying x + -3.5 = 6.873863542 Reorder the terms: -3.5 + x = 6.873863542 Solving -3.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 6.873863542 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.873863542 + 3.5 x = 6.873863542 + 3.5 Combine like terms: 6.873863542 + 3.5 = 10.373863542 x = 10.373863542 Simplifying x = 10.373863542Subproblem 2
x + -3.5 = -6.873863542 Simplifying x + -3.5 = -6.873863542 Reorder the terms: -3.5 + x = -6.873863542 Solving -3.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -6.873863542 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.873863542 + 3.5 x = -6.873863542 + 3.5 Combine like terms: -6.873863542 + 3.5 = -3.373863542 x = -3.373863542 Simplifying x = -3.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.373863542, -3.373863542}
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