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Simplifying 3x2 + 12x + -61 = 0 Reorder the terms: -61 + 12x + 3x2 = 0 Solving -61 + 12x + 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 + 4x + x2 = 0 Move the constant term to the right: Add '20.33333333' to each side of the equation. -20.33333333 + 4x + 20.33333333 + x2 = 0 + 20.33333333 Reorder the terms: -20.33333333 + 20.33333333 + 4x + x2 = 0 + 20.33333333 Combine like terms: -20.33333333 + 20.33333333 = 0.00000000 0.00000000 + 4x + x2 = 0 + 20.33333333 4x + x2 = 0 + 20.33333333 Combine like terms: 0 + 20.33333333 = 20.33333333 4x + x2 = 20.33333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 20.33333333 + 4 Reorder the terms: 4 + 4x + x2 = 20.33333333 + 4 Combine like terms: 20.33333333 + 4 = 24.33333333 4 + 4x + x2 = 24.33333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 24.33333333 Calculate the square root of the right side: 4.932882862 Break this problem into two subproblems by setting (x + 2) equal to 4.932882862 and -4.932882862.Subproblem 1
x + 2 = 4.932882862 Simplifying x + 2 = 4.932882862 Reorder the terms: 2 + x = 4.932882862 Solving 2 + x = 4.932882862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.932882862 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.932882862 + -2 x = 4.932882862 + -2 Combine like terms: 4.932882862 + -2 = 2.932882862 x = 2.932882862 Simplifying x = 2.932882862Subproblem 2
x + 2 = -4.932882862 Simplifying x + 2 = -4.932882862 Reorder the terms: 2 + x = -4.932882862 Solving 2 + x = -4.932882862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.932882862 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.932882862 + -2 x = -4.932882862 + -2 Combine like terms: -4.932882862 + -2 = -6.932882862 x = -6.932882862 Simplifying x = -6.932882862Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.932882862, -6.932882862}
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