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Simplifying 2x2 + 21x + 24 = 0 Reorder the terms: 24 + 21x + 2x2 = 0 Solving 24 + 21x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12 + 10.5x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 10.5x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 10.5x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 10.5x + x2 = 0 + -12 10.5x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 10.5x + x2 = -12 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = -12 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = -12 + 27.5625 Combine like terms: -12 + 27.5625 = 15.5625 27.5625 + 10.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + 5.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + 5.25 = 3.94493346 Simplifying x + 5.25 = 3.94493346 Reorder the terms: 5.25 + x = 3.94493346 Solving 5.25 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 3.94493346 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 3.94493346 + -5.25 x = 3.94493346 + -5.25 Combine like terms: 3.94493346 + -5.25 = -1.30506654 x = -1.30506654 Simplifying x = -1.30506654Subproblem 2
x + 5.25 = -3.94493346 Simplifying x + 5.25 = -3.94493346 Reorder the terms: 5.25 + x = -3.94493346 Solving 5.25 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -3.94493346 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -3.94493346 + -5.25 x = -3.94493346 + -5.25 Combine like terms: -3.94493346 + -5.25 = -9.19493346 x = -9.19493346 Simplifying x = -9.19493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.30506654, -9.19493346}
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