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Simplifying x2 = 10x + 35 Reorder the terms: x2 = 35 + 10x Solving x2 = 35 + 10x Solving for variable 'x'. Reorder the terms: -35 + -10x + x2 = 35 + 10x + -35 + -10x Reorder the terms: -35 + -10x + x2 = 35 + -35 + 10x + -10x Combine like terms: 35 + -35 = 0 -35 + -10x + x2 = 0 + 10x + -10x -35 + -10x + x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -35 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -10x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -10x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -10x + x2 = 0 + 35 -10x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -10x + x2 = 35 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 35 + 25 Reorder the terms: 25 + -10x + x2 = 35 + 25 Combine like terms: 35 + 25 = 60 25 + -10x + x2 = 60 Factor a perfect square on the left side: (x + -5)(x + -5) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -5) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -5 = 7.745966692 Simplifying x + -5 = 7.745966692 Reorder the terms: -5 + x = 7.745966692 Solving -5 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.745966692 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.745966692 + 5 x = 7.745966692 + 5 Combine like terms: 7.745966692 + 5 = 12.745966692 x = 12.745966692 Simplifying x = 12.745966692Subproblem 2
x + -5 = -7.745966692 Simplifying x + -5 = -7.745966692 Reorder the terms: -5 + x = -7.745966692 Solving -5 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.745966692 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.745966692 + 5 x = -7.745966692 + 5 Combine like terms: -7.745966692 + 5 = -2.745966692 x = -2.745966692 Simplifying x = -2.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.745966692, -2.745966692}
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