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Simplifying x2 + -23x + 45 = 0 Reorder the terms: 45 + -23x + x2 = 0 Solving 45 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -23x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -23x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -23x + x2 = 0 + -45 -23x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -23x + x2 = -45 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 = -45 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -45 + 132.25 Combine like terms: -45 + 132.25 = 87.25 132.25 + -23x + x2 = 87.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 87.25 Calculate the square root of the right side: 9.340770846 Break this problem into two subproblems by setting (x + -11.5) equal to 9.340770846 and -9.340770846.Subproblem 1
x + -11.5 = 9.340770846 Simplifying x + -11.5 = 9.340770846 Reorder the terms: -11.5 + x = 9.340770846 Solving -11.5 + x = 9.340770846 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 = 9.340770846 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 9.340770846 + 11.5 x = 9.340770846 + 11.5 Combine like terms: 9.340770846 + 11.5 = 20.840770846 x = 20.840770846 Simplifying x = 20.840770846Subproblem 2
x + -11.5 = -9.340770846 Simplifying x + -11.5 = -9.340770846 Reorder the terms: -11.5 + x = -9.340770846 Solving -11.5 + x = -9.340770846 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 = -9.340770846 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -9.340770846 + 11.5 x = -9.340770846 + 11.5 Combine like terms: -9.340770846 + 11.5 = 2.159229154 x = 2.159229154 Simplifying x = 2.159229154Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.840770846, 2.159229154}
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