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Simplifying x2 + -23x + 26 = 0 Reorder the terms: 26 + -23x + x2 = 0 Solving 26 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -23x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -23x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -23x + x2 = 0 + -26 -23x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -23x + x2 = -26 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -26 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -26 + 132.25 Combine like terms: -26 + 132.25 = 106.25 132.25 + -23x + x2 = 106.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + -11.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + -11.5 = 10.307764064 Simplifying x + -11.5 = 10.307764064 Reorder the terms: -11.5 + x = 10.307764064 Solving -11.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 10.307764064 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 10.307764064 + 11.5 x = 10.307764064 + 11.5 Combine like terms: 10.307764064 + 11.5 = 21.807764064 x = 21.807764064 Simplifying x = 21.807764064Subproblem 2
x + -11.5 = -10.307764064 Simplifying x + -11.5 = -10.307764064 Reorder the terms: -11.5 + x = -10.307764064 Solving -11.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -10.307764064 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -10.307764064 + 11.5 x = -10.307764064 + 11.5 Combine like terms: -10.307764064 + 11.5 = 1.192235936 x = 1.192235936 Simplifying x = 1.192235936Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.807764064, 1.192235936}
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