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Simplifying 5x2 + 60x + 174 = 0 Reorder the terms: 174 + 60x + 5x2 = 0 Solving 174 + 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'. 34.8 + 12x + x2 = 0 Move the constant term to the right: Add '-34.8' to each side of the equation. 34.8 + 12x + -34.8 + x2 = 0 + -34.8 Reorder the terms: 34.8 + -34.8 + 12x + x2 = 0 + -34.8 Combine like terms: 34.8 + -34.8 = 0.0 0.0 + 12x + x2 = 0 + -34.8 12x + x2 = 0 + -34.8 Combine like terms: 0 + -34.8 = -34.8 12x + x2 = -34.8 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 = -34.8 + 36 Reorder the terms: 36 + 12x + x2 = -34.8 + 36 Combine like terms: -34.8 + 36 = 1.2 36 + 12x + x2 = 1.2 Factor a perfect square on the left side: (x + 6)(x + 6) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (x + 6) equal to 1.095445115 and -1.095445115.Subproblem 1
x + 6 = 1.095445115 Simplifying x + 6 = 1.095445115 Reorder the terms: 6 + x = 1.095445115 Solving 6 + x = 1.095445115 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 = 1.095445115 + -6 Combine like terms: 6 + -6 = 0 0 + x = 1.095445115 + -6 x = 1.095445115 + -6 Combine like terms: 1.095445115 + -6 = -4.904554885 x = -4.904554885 Simplifying x = -4.904554885Subproblem 2
x + 6 = -1.095445115 Simplifying x + 6 = -1.095445115 Reorder the terms: 6 + x = -1.095445115 Solving 6 + x = -1.095445115 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 = -1.095445115 + -6 Combine like terms: 6 + -6 = 0 0 + x = -1.095445115 + -6 x = -1.095445115 + -6 Combine like terms: -1.095445115 + -6 = -7.095445115 x = -7.095445115 Simplifying x = -7.095445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.904554885, -7.095445115}
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