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Simplifying 2x2 + 21x + -378 = 0 Reorder the terms: -378 + 21x + 2x2 = 0 Solving -378 + 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'. -189 + 10.5x + x2 = 0 Move the constant term to the right: Add '189' to each side of the equation. -189 + 10.5x + 189 + x2 = 0 + 189 Reorder the terms: -189 + 189 + 10.5x + x2 = 0 + 189 Combine like terms: -189 + 189 = 0 0 + 10.5x + x2 = 0 + 189 10.5x + x2 = 0 + 189 Combine like terms: 0 + 189 = 189 10.5x + x2 = 189 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 = 189 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 189 + 27.5625 Combine like terms: 189 + 27.5625 = 216.5625 27.5625 + 10.5x + x2 = 216.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 216.5625 Calculate the square root of the right side: 14.716062653 Break this problem into two subproblems by setting (x + 5.25) equal to 14.716062653 and -14.716062653.Subproblem 1
x + 5.25 = 14.716062653 Simplifying x + 5.25 = 14.716062653 Reorder the terms: 5.25 + x = 14.716062653 Solving 5.25 + x = 14.716062653 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 = 14.716062653 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 14.716062653 + -5.25 x = 14.716062653 + -5.25 Combine like terms: 14.716062653 + -5.25 = 9.466062653 x = 9.466062653 Simplifying x = 9.466062653Subproblem 2
x + 5.25 = -14.716062653 Simplifying x + 5.25 = -14.716062653 Reorder the terms: 5.25 + x = -14.716062653 Solving 5.25 + x = -14.716062653 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 = -14.716062653 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -14.716062653 + -5.25 x = -14.716062653 + -5.25 Combine like terms: -14.716062653 + -5.25 = -19.966062653 x = -19.966062653 Simplifying x = -19.966062653Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.466062653, -19.966062653}
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