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Simplifying x2 + -21x + 23 = 0 Reorder the terms: 23 + -21x + x2 = 0 Solving 23 + -21x + 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 + -21x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -21x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -21x + x2 = 0 + -23 -21x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -21x + x2 = -23 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -23 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -23 + 110.25 Combine like terms: -23 + 110.25 = 87.25 110.25 + -21x + x2 = 87.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 87.25 Calculate the square root of the right side: 9.340770846 Break this problem into two subproblems by setting (x + -10.5) equal to 9.340770846 and -9.340770846.Subproblem 1
x + -10.5 = 9.340770846 Simplifying x + -10.5 = 9.340770846 Reorder the terms: -10.5 + x = 9.340770846 Solving -10.5 + x = 9.340770846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 9.340770846 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.340770846 + 10.5 x = 9.340770846 + 10.5 Combine like terms: 9.340770846 + 10.5 = 19.840770846 x = 19.840770846 Simplifying x = 19.840770846Subproblem 2
x + -10.5 = -9.340770846 Simplifying x + -10.5 = -9.340770846 Reorder the terms: -10.5 + x = -9.340770846 Solving -10.5 + x = -9.340770846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -9.340770846 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.340770846 + 10.5 x = -9.340770846 + 10.5 Combine like terms: -9.340770846 + 10.5 = 1.159229154 x = 1.159229154 Simplifying x = 1.159229154Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.840770846, 1.159229154}
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