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Simplifying -1x2 + 21x + 24 = 0 Reorder the terms: 24 + 21x + -1x2 = 0 Solving 24 + 21x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + -21x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -21x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -21x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -21x + x2 = 0 + 24 -21x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -21x + x2 = 24 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 = 24 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 24 + 110.25 Combine like terms: 24 + 110.25 = 134.25 110.25 + -21x + x2 = 134.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (x + -10.5) equal to 11.586630226 and -11.586630226.Subproblem 1
x + -10.5 = 11.586630226 Simplifying x + -10.5 = 11.586630226 Reorder the terms: -10.5 + x = 11.586630226 Solving -10.5 + x = 11.586630226 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 = 11.586630226 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 11.586630226 + 10.5 x = 11.586630226 + 10.5 Combine like terms: 11.586630226 + 10.5 = 22.086630226 x = 22.086630226 Simplifying x = 22.086630226Subproblem 2
x + -10.5 = -11.586630226 Simplifying x + -10.5 = -11.586630226 Reorder the terms: -10.5 + x = -11.586630226 Solving -10.5 + x = -11.586630226 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 = -11.586630226 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -11.586630226 + 10.5 x = -11.586630226 + 10.5 Combine like terms: -11.586630226 + 10.5 = -1.086630226 x = -1.086630226 Simplifying x = -1.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.086630226, -1.086630226}
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