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Simplifying 3x2 + 85x + 9 = 0 Reorder the terms: 9 + 85x + 3x2 = 0 Solving 9 + 85x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + 28.33333333x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 28.33333333x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 28.33333333x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 28.33333333x + x2 = 0 + -3 28.33333333x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 28.33333333x + x2 = -3 The x term is 28.33333333x. Take half its coefficient (14.16666667). Square it (200.6944445) and add it to both sides. Add '200.6944445' to each side of the equation. 28.33333333x + 200.6944445 + x2 = -3 + 200.6944445 Reorder the terms: 200.6944445 + 28.33333333x + x2 = -3 + 200.6944445 Combine like terms: -3 + 200.6944445 = 197.6944445 200.6944445 + 28.33333333x + x2 = 197.6944445 Factor a perfect square on the left side: (x + 14.16666667)(x + 14.16666667) = 197.6944445 Calculate the square root of the right side: 14.060385645 Break this problem into two subproblems by setting (x + 14.16666667) equal to 14.060385645 and -14.060385645.Subproblem 1
x + 14.16666667 = 14.060385645 Simplifying x + 14.16666667 = 14.060385645 Reorder the terms: 14.16666667 + x = 14.060385645 Solving 14.16666667 + x = 14.060385645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.16666667' to each side of the equation. 14.16666667 + -14.16666667 + x = 14.060385645 + -14.16666667 Combine like terms: 14.16666667 + -14.16666667 = 0.00000000 0.00000000 + x = 14.060385645 + -14.16666667 x = 14.060385645 + -14.16666667 Combine like terms: 14.060385645 + -14.16666667 = -0.106281025 x = -0.106281025 Simplifying x = -0.106281025Subproblem 2
x + 14.16666667 = -14.060385645 Simplifying x + 14.16666667 = -14.060385645 Reorder the terms: 14.16666667 + x = -14.060385645 Solving 14.16666667 + x = -14.060385645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.16666667' to each side of the equation. 14.16666667 + -14.16666667 + x = -14.060385645 + -14.16666667 Combine like terms: 14.16666667 + -14.16666667 = 0.00000000 0.00000000 + x = -14.060385645 + -14.16666667 x = -14.060385645 + -14.16666667 Combine like terms: -14.060385645 + -14.16666667 = -28.227052315 x = -28.227052315 Simplifying x = -28.227052315Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.106281025, -28.227052315}
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