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Simplifying 5x2 + 60x + 9 = 0 Reorder the terms: 9 + 60x + 5x2 = 0 Solving 9 + 60x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 12x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 12x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 12x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 12x + x2 = 0 + -1.8 12x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 12x + x2 = -1.8 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 = -1.8 + 36 Reorder the terms: 36 + 12x + x2 = -1.8 + 36 Combine like terms: -1.8 + 36 = 34.2 36 + 12x + x2 = 34.2 Factor a perfect square on the left side: (x + 6)(x + 6) = 34.2 Calculate the square root of the right side: 5.848076607 Break this problem into two subproblems by setting (x + 6) equal to 5.848076607 and -5.848076607.Subproblem 1
x + 6 = 5.848076607 Simplifying x + 6 = 5.848076607 Reorder the terms: 6 + x = 5.848076607 Solving 6 + x = 5.848076607 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 = 5.848076607 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.848076607 + -6 x = 5.848076607 + -6 Combine like terms: 5.848076607 + -6 = -0.151923393 x = -0.151923393 Simplifying x = -0.151923393Subproblem 2
x + 6 = -5.848076607 Simplifying x + 6 = -5.848076607 Reorder the terms: 6 + x = -5.848076607 Solving 6 + x = -5.848076607 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 = -5.848076607 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.848076607 + -6 x = -5.848076607 + -6 Combine like terms: -5.848076607 + -6 = -11.848076607 x = -11.848076607 Simplifying x = -11.848076607Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.151923393, -11.848076607}
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