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Simplifying x2 + -13x + 37 = 0 Reorder the terms: 37 + -13x + x2 = 0 Solving 37 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + -13x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + -13x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -13x + x2 = 0 + -37 -13x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 -13x + x2 = -37 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 = -37 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -37 + 42.25 Combine like terms: -37 + 42.25 = 5.25 42.25 + -13x + x2 = 5.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -6.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -6.5 = 2.291287847 Simplifying x + -6.5 = 2.291287847 Reorder the terms: -6.5 + x = 2.291287847 Solving -6.5 + x = 2.291287847 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 = 2.291287847 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 2.291287847 + 6.5 x = 2.291287847 + 6.5 Combine like terms: 2.291287847 + 6.5 = 8.791287847 x = 8.791287847 Simplifying x = 8.791287847Subproblem 2
x + -6.5 = -2.291287847 Simplifying x + -6.5 = -2.291287847 Reorder the terms: -6.5 + x = -2.291287847 Solving -6.5 + x = -2.291287847 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 = -2.291287847 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -2.291287847 + 6.5 x = -2.291287847 + 6.5 Combine like terms: -2.291287847 + 6.5 = 4.208712153 x = 4.208712153 Simplifying x = 4.208712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.791287847, 4.208712153}
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