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Simplifying 5x2 + 60x + 36 = 0 Reorder the terms: 36 + 60x + 5x2 = 0 Solving 36 + 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'. 7.2 + 12x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + 12x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + 12x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + 12x + x2 = 0 + -7.2 12x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 12x + x2 = -7.2 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 = -7.2 + 36 Reorder the terms: 36 + 12x + x2 = -7.2 + 36 Combine like terms: -7.2 + 36 = 28.8 36 + 12x + x2 = 28.8 Factor a perfect square on the left side: (x + 6)(x + 6) = 28.8 Calculate the square root of the right side: 5.366563146 Break this problem into two subproblems by setting (x + 6) equal to 5.366563146 and -5.366563146.Subproblem 1
x + 6 = 5.366563146 Simplifying x + 6 = 5.366563146 Reorder the terms: 6 + x = 5.366563146 Solving 6 + x = 5.366563146 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 = 5.366563146 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.366563146 + -6 x = 5.366563146 + -6 Combine like terms: 5.366563146 + -6 = -0.633436854 x = -0.633436854 Simplifying x = -0.633436854Subproblem 2
x + 6 = -5.366563146 Simplifying x + 6 = -5.366563146 Reorder the terms: 6 + x = -5.366563146 Solving 6 + x = -5.366563146 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 = -5.366563146 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.366563146 + -6 x = -5.366563146 + -6 Combine like terms: -5.366563146 + -6 = -11.366563146 x = -11.366563146 Simplifying x = -11.366563146Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.633436854, -11.366563146}
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