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Simplifying -18x2 + 51x + 8 = 0 Reorder the terms: 8 + 51x + -18x2 = 0 Solving 8 + 51x + -18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.4444444444 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -2.833333333x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -2.833333333x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -2.833333333x + x2 = 0 + 0.4444444444 -2.833333333x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -2.833333333x + x2 = 0.4444444444 The x term is -2.833333333x. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x + 2.006944445 + x2 = 0.4444444444 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = 0.4444444444 + 2.006944445 Combine like terms: 0.4444444444 + 2.006944445 = 2.4513888894 2.006944445 + -2.833333333x + x2 = 2.4513888894 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 2.4513888894 Calculate the square root of the right side: 1.565691186 Break this problem into two subproblems by setting (x + -1.416666667) equal to 1.565691186 and -1.565691186.Subproblem 1
x + -1.416666667 = 1.565691186 Simplifying x + -1.416666667 = 1.565691186 Reorder the terms: -1.416666667 + x = 1.565691186 Solving -1.416666667 + x = 1.565691186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = 1.565691186 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 1.565691186 + 1.416666667 x = 1.565691186 + 1.416666667 Combine like terms: 1.565691186 + 1.416666667 = 2.982357853 x = 2.982357853 Simplifying x = 2.982357853Subproblem 2
x + -1.416666667 = -1.565691186 Simplifying x + -1.416666667 = -1.565691186 Reorder the terms: -1.416666667 + x = -1.565691186 Solving -1.416666667 + x = -1.565691186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = -1.565691186 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -1.565691186 + 1.416666667 x = -1.565691186 + 1.416666667 Combine like terms: -1.565691186 + 1.416666667 = -0.149024519 x = -0.149024519 Simplifying x = -0.149024519Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.982357853, -0.149024519}
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