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Simplifying x2 + 13x + 40 = 42756 Reorder the terms: 40 + 13x + x2 = 42756 Solving 40 + 13x + x2 = 42756 Solving for variable 'x'. Reorder the terms: 40 + -42756 + 13x + x2 = 42756 + -42756 Combine like terms: 40 + -42756 = -42716 -42716 + 13x + x2 = 42756 + -42756 Combine like terms: 42756 + -42756 = 0 -42716 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42716' to each side of the equation. -42716 + 13x + 42716 + x2 = 0 + 42716 Reorder the terms: -42716 + 42716 + 13x + x2 = 0 + 42716 Combine like terms: -42716 + 42716 = 0 0 + 13x + x2 = 0 + 42716 13x + x2 = 0 + 42716 Combine like terms: 0 + 42716 = 42716 13x + x2 = 42716 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 = 42716 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 42716 + 42.25 Combine like terms: 42716 + 42.25 = 42758.25 42.25 + 13x + x2 = 42758.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 42758.25 Calculate the square root of the right side: 206.780680916 Break this problem into two subproblems by setting (x + 6.5) equal to 206.780680916 and -206.780680916.Subproblem 1
x + 6.5 = 206.780680916 Simplifying x + 6.5 = 206.780680916 Reorder the terms: 6.5 + x = 206.780680916 Solving 6.5 + x = 206.780680916 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 = 206.780680916 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 206.780680916 + -6.5 x = 206.780680916 + -6.5 Combine like terms: 206.780680916 + -6.5 = 200.280680916 x = 200.280680916 Simplifying x = 200.280680916Subproblem 2
x + 6.5 = -206.780680916 Simplifying x + 6.5 = -206.780680916 Reorder the terms: 6.5 + x = -206.780680916 Solving 6.5 + x = -206.780680916 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 = -206.780680916 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -206.780680916 + -6.5 x = -206.780680916 + -6.5 Combine like terms: -206.780680916 + -6.5 = -213.280680916 x = -213.280680916 Simplifying x = -213.280680916Solution
The solution to the problem is based on the solutions from the subproblems. x = {200.280680916, -213.280680916}
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