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Simplifying 3x2 + 36x + 76 = 0 Reorder the terms: 76 + 36x + 3x2 = 0 Solving 76 + 36x + 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'. 25.33333333 + 12x + x2 = 0 Move the constant term to the right: Add '-25.33333333' to each side of the equation. 25.33333333 + 12x + -25.33333333 + x2 = 0 + -25.33333333 Reorder the terms: 25.33333333 + -25.33333333 + 12x + x2 = 0 + -25.33333333 Combine like terms: 25.33333333 + -25.33333333 = 0.00000000 0.00000000 + 12x + x2 = 0 + -25.33333333 12x + x2 = 0 + -25.33333333 Combine like terms: 0 + -25.33333333 = -25.33333333 12x + x2 = -25.33333333 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -25.33333333 + 36 Reorder the terms: 36 + 12x + x2 = -25.33333333 + 36 Combine like terms: -25.33333333 + 36 = 10.66666667 36 + 12x + x2 = 10.66666667 Factor a perfect square on the left side: (x + 6)(x + 6) = 10.66666667 Calculate the square root of the right side: 3.265986324 Break this problem into two subproblems by setting (x + 6) equal to 3.265986324 and -3.265986324.Subproblem 1
x + 6 = 3.265986324 Simplifying x + 6 = 3.265986324 Reorder the terms: 6 + x = 3.265986324 Solving 6 + x = 3.265986324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 3.265986324 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.265986324 + -6 x = 3.265986324 + -6 Combine like terms: 3.265986324 + -6 = -2.734013676 x = -2.734013676 Simplifying x = -2.734013676Subproblem 2
x + 6 = -3.265986324 Simplifying x + 6 = -3.265986324 Reorder the terms: 6 + x = -3.265986324 Solving 6 + x = -3.265986324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -3.265986324 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.265986324 + -6 x = -3.265986324 + -6 Combine like terms: -3.265986324 + -6 = -9.265986324 x = -9.265986324 Simplifying x = -9.265986324Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.734013676, -9.265986324}
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