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Simplifying x2 = 65 + 7x Solving x2 = 65 + 7x Solving for variable 'x'. Reorder the terms: -65 + -7x + x2 = 65 + 7x + -65 + -7x Reorder the terms: -65 + -7x + x2 = 65 + -65 + 7x + -7x Combine like terms: 65 + -65 = 0 -65 + -7x + x2 = 0 + 7x + -7x -65 + -7x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -65 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + -7x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + -7x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -7x + x2 = 0 + 65 -7x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 -7x + x2 = 65 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 = 65 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 65 + 12.25 Combine like terms: 65 + 12.25 = 77.25 12.25 + -7x + x2 = 77.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 77.25 Calculate the square root of the right side: 8.789197916 Break this problem into two subproblems by setting (x + -3.5) equal to 8.789197916 and -8.789197916.Subproblem 1
x + -3.5 = 8.789197916 Simplifying x + -3.5 = 8.789197916 Reorder the terms: -3.5 + x = 8.789197916 Solving -3.5 + x = 8.789197916 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 = 8.789197916 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 8.789197916 + 3.5 x = 8.789197916 + 3.5 Combine like terms: 8.789197916 + 3.5 = 12.289197916 x = 12.289197916 Simplifying x = 12.289197916Subproblem 2
x + -3.5 = -8.789197916 Simplifying x + -3.5 = -8.789197916 Reorder the terms: -3.5 + x = -8.789197916 Solving -3.5 + x = -8.789197916 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 = -8.789197916 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -8.789197916 + 3.5 x = -8.789197916 + 3.5 Combine like terms: -8.789197916 + 3.5 = -5.289197916 x = -5.289197916 Simplifying x = -5.289197916Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.289197916, -5.289197916}
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