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Simplifying x2 + -24x + 21 = 0 Reorder the terms: 21 + -24x + x2 = 0 Solving 21 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -24x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -24x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -24x + x2 = 0 + -21 -24x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -24x + x2 = -21 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -21 + 144 Reorder the terms: 144 + -24x + x2 = -21 + 144 Combine like terms: -21 + 144 = 123 144 + -24x + x2 = 123 Factor a perfect square on the left side: (x + -12)(x + -12) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (x + -12) equal to 11.090536506 and -11.090536506.Subproblem 1
x + -12 = 11.090536506 Simplifying x + -12 = 11.090536506 Reorder the terms: -12 + x = 11.090536506 Solving -12 + x = 11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.090536506 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.090536506 + 12 x = 11.090536506 + 12 Combine like terms: 11.090536506 + 12 = 23.090536506 x = 23.090536506 Simplifying x = 23.090536506Subproblem 2
x + -12 = -11.090536506 Simplifying x + -12 = -11.090536506 Reorder the terms: -12 + x = -11.090536506 Solving -12 + x = -11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.090536506 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.090536506 + 12 x = -11.090536506 + 12 Combine like terms: -11.090536506 + 12 = 0.909463494 x = 0.909463494 Simplifying x = 0.909463494Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.090536506, 0.909463494}
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