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Simplifying x2 = 13x + 6 Reorder the terms: x2 = 6 + 13x Solving x2 = 6 + 13x Solving for variable 'x'. Reorder the terms: -6 + -13x + x2 = 6 + 13x + -6 + -13x Reorder the terms: -6 + -13x + x2 = 6 + -6 + 13x + -13x Combine like terms: 6 + -6 = 0 -6 + -13x + x2 = 0 + 13x + -13x -6 + -13x + x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -6 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -13x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -13x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -13x + x2 = 0 + 6 -13x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -13x + x2 = 6 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 6 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 6 + 42.25 Combine like terms: 6 + 42.25 = 48.25 42.25 + -13x + x2 = 48.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -6.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -6.5 = 6.946221995 Simplifying x + -6.5 = 6.946221995 Reorder the terms: -6.5 + x = 6.946221995 Solving -6.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.946221995 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.946221995 + 6.5 x = 6.946221995 + 6.5 Combine like terms: 6.946221995 + 6.5 = 13.446221995 x = 13.446221995 Simplifying x = 13.446221995Subproblem 2
x + -6.5 = -6.946221995 Simplifying x + -6.5 = -6.946221995 Reorder the terms: -6.5 + x = -6.946221995 Solving -6.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.946221995 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.946221995 + 6.5 x = -6.946221995 + 6.5 Combine like terms: -6.946221995 + 6.5 = -0.446221995 x = -0.446221995 Simplifying x = -0.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.446221995, -0.446221995}
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