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Simplifying x2 + -13x + 23 = 0 Reorder the terms: 23 + -13x + x2 = 0 Solving 23 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + -13x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -13x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -13x + x2 = 0 + -23 -13x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -13x + x2 = -23 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 = -23 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -23 + 42.25 Combine like terms: -23 + 42.25 = 19.25 42.25 + -13x + x2 = 19.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -6.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -6.5 = 4.387482194 Simplifying x + -6.5 = 4.387482194 Reorder the terms: -6.5 + x = 4.387482194 Solving -6.5 + x = 4.387482194 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 = 4.387482194 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 4.387482194 + 6.5 x = 4.387482194 + 6.5 Combine like terms: 4.387482194 + 6.5 = 10.887482194 x = 10.887482194 Simplifying x = 10.887482194Subproblem 2
x + -6.5 = -4.387482194 Simplifying x + -6.5 = -4.387482194 Reorder the terms: -6.5 + x = -4.387482194 Solving -6.5 + x = -4.387482194 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 = -4.387482194 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -4.387482194 + 6.5 x = -4.387482194 + 6.5 Combine like terms: -4.387482194 + 6.5 = 2.112517806 x = 2.112517806 Simplifying x = 2.112517806Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.887482194, 2.112517806}
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