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Simplifying 3x2 + 9x + -61 = 0 Reorder the terms: -61 + 9x + 3x2 = 0 Solving -61 + 9x + 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'. -20.33333333 + 3x + x2 = 0 Move the constant term to the right: Add '20.33333333' to each side of the equation. -20.33333333 + 3x + 20.33333333 + x2 = 0 + 20.33333333 Reorder the terms: -20.33333333 + 20.33333333 + 3x + x2 = 0 + 20.33333333 Combine like terms: -20.33333333 + 20.33333333 = 0.00000000 0.00000000 + 3x + x2 = 0 + 20.33333333 3x + x2 = 0 + 20.33333333 Combine like terms: 0 + 20.33333333 = 20.33333333 3x + x2 = 20.33333333 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 20.33333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 20.33333333 + 2.25 Combine like terms: 20.33333333 + 2.25 = 22.58333333 2.25 + 3x + x2 = 22.58333333 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 22.58333333 Calculate the square root of the right side: 4.752192476 Break this problem into two subproblems by setting (x + 1.5) equal to 4.752192476 and -4.752192476.Subproblem 1
x + 1.5 = 4.752192476 Simplifying x + 1.5 = 4.752192476 Reorder the terms: 1.5 + x = 4.752192476 Solving 1.5 + x = 4.752192476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.752192476 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.752192476 + -1.5 x = 4.752192476 + -1.5 Combine like terms: 4.752192476 + -1.5 = 3.252192476 x = 3.252192476 Simplifying x = 3.252192476Subproblem 2
x + 1.5 = -4.752192476 Simplifying x + 1.5 = -4.752192476 Reorder the terms: 1.5 + x = -4.752192476 Solving 1.5 + x = -4.752192476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.752192476 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.752192476 + -1.5 x = -4.752192476 + -1.5 Combine like terms: -4.752192476 + -1.5 = -6.252192476 x = -6.252192476 Simplifying x = -6.252192476Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.252192476, -6.252192476}
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