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Simplifying 2x2 + 21x + -8.1 = 0 Reorder the terms: -8.1 + 21x + 2x2 = 0 Solving -8.1 + 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'. -4.05 + 10.5x + x2 = 0 Move the constant term to the right: Add '4.05' to each side of the equation. -4.05 + 10.5x + 4.05 + x2 = 0 + 4.05 Reorder the terms: -4.05 + 4.05 + 10.5x + x2 = 0 + 4.05 Combine like terms: -4.05 + 4.05 = 0.00 0.00 + 10.5x + x2 = 0 + 4.05 10.5x + x2 = 0 + 4.05 Combine like terms: 0 + 4.05 = 4.05 10.5x + x2 = 4.05 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 = 4.05 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 4.05 + 27.5625 Combine like terms: 4.05 + 27.5625 = 31.6125 27.5625 + 10.5x + x2 = 31.6125 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 31.6125 Calculate the square root of the right side: 5.622499444 Break this problem into two subproblems by setting (x + 5.25) equal to 5.622499444 and -5.622499444.Subproblem 1
x + 5.25 = 5.622499444 Simplifying x + 5.25 = 5.622499444 Reorder the terms: 5.25 + x = 5.622499444 Solving 5.25 + x = 5.622499444 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 = 5.622499444 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 5.622499444 + -5.25 x = 5.622499444 + -5.25 Combine like terms: 5.622499444 + -5.25 = 0.372499444 x = 0.372499444 Simplifying x = 0.372499444Subproblem 2
x + 5.25 = -5.622499444 Simplifying x + 5.25 = -5.622499444 Reorder the terms: 5.25 + x = -5.622499444 Solving 5.25 + x = -5.622499444 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 = -5.622499444 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -5.622499444 + -5.25 x = -5.622499444 + -5.25 Combine like terms: -5.622499444 + -5.25 = -10.872499444 x = -10.872499444 Simplifying x = -10.872499444Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.372499444, -10.872499444}
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