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Simplifying 3x2 + 36x + -80 = 0 Reorder the terms: -80 + 36x + 3x2 = 0 Solving -80 + 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'. -26.66666667 + 12x + x2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + 12x + 26.66666667 + x2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + 12x + x2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + 12x + x2 = 0 + 26.66666667 12x + x2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 12x + x2 = 26.66666667 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 = 26.66666667 + 36 Reorder the terms: 36 + 12x + x2 = 26.66666667 + 36 Combine like terms: 26.66666667 + 36 = 62.66666667 36 + 12x + x2 = 62.66666667 Factor a perfect square on the left side: (x + 6)(x + 6) = 62.66666667 Calculate the square root of the right side: 7.916228058 Break this problem into two subproblems by setting (x + 6) equal to 7.916228058 and -7.916228058.Subproblem 1
x + 6 = 7.916228058 Simplifying x + 6 = 7.916228058 Reorder the terms: 6 + x = 7.916228058 Solving 6 + x = 7.916228058 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 = 7.916228058 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.916228058 + -6 x = 7.916228058 + -6 Combine like terms: 7.916228058 + -6 = 1.916228058 x = 1.916228058 Simplifying x = 1.916228058Subproblem 2
x + 6 = -7.916228058 Simplifying x + 6 = -7.916228058 Reorder the terms: 6 + x = -7.916228058 Solving 6 + x = -7.916228058 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 = -7.916228058 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.916228058 + -6 x = -7.916228058 + -6 Combine like terms: -7.916228058 + -6 = -13.916228058 x = -13.916228058 Simplifying x = -13.916228058Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.916228058, -13.916228058}
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