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Simplifying x2 = 35x + 5 Reorder the terms: x2 = 5 + 35x Solving x2 = 5 + 35x Solving for variable 'x'. Reorder the terms: -5 + -35x + x2 = 5 + 35x + -5 + -35x Reorder the terms: -5 + -35x + x2 = 5 + -5 + 35x + -35x Combine like terms: 5 + -5 = 0 -5 + -35x + x2 = 0 + 35x + -35x -5 + -35x + x2 = 35x + -35x Combine like terms: 35x + -35x = 0 -5 + -35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -35x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -35x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -35x + x2 = 0 + 5 -35x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -35x + x2 = 5 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = 5 + 306.25 Reorder the terms: 306.25 + -35x + x2 = 5 + 306.25 Combine like terms: 5 + 306.25 = 311.25 306.25 + -35x + x2 = 311.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 311.25 Calculate the square root of the right side: 17.642278764 Break this problem into two subproblems by setting (x + -17.5) equal to 17.642278764 and -17.642278764.Subproblem 1
x + -17.5 = 17.642278764 Simplifying x + -17.5 = 17.642278764 Reorder the terms: -17.5 + x = 17.642278764 Solving -17.5 + x = 17.642278764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 17.642278764 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 17.642278764 + 17.5 x = 17.642278764 + 17.5 Combine like terms: 17.642278764 + 17.5 = 35.142278764 x = 35.142278764 Simplifying x = 35.142278764Subproblem 2
x + -17.5 = -17.642278764 Simplifying x + -17.5 = -17.642278764 Reorder the terms: -17.5 + x = -17.642278764 Solving -17.5 + x = -17.642278764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -17.642278764 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -17.642278764 + 17.5 x = -17.642278764 + 17.5 Combine like terms: -17.642278764 + 17.5 = -0.142278764 x = -0.142278764 Simplifying x = -0.142278764Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.142278764, -0.142278764}
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