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Simplifying 5x2 + 60x + 172 = 0 Reorder the terms: 172 + 60x + 5x2 = 0 Solving 172 + 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'. 34.4 + 12x + x2 = 0 Move the constant term to the right: Add '-34.4' to each side of the equation. 34.4 + 12x + -34.4 + x2 = 0 + -34.4 Reorder the terms: 34.4 + -34.4 + 12x + x2 = 0 + -34.4 Combine like terms: 34.4 + -34.4 = 0.0 0.0 + 12x + x2 = 0 + -34.4 12x + x2 = 0 + -34.4 Combine like terms: 0 + -34.4 = -34.4 12x + x2 = -34.4 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 = -34.4 + 36 Reorder the terms: 36 + 12x + x2 = -34.4 + 36 Combine like terms: -34.4 + 36 = 1.6 36 + 12x + x2 = 1.6 Factor a perfect square on the left side: (x + 6)(x + 6) = 1.6 Calculate the square root of the right side: 1.264911064 Break this problem into two subproblems by setting (x + 6) equal to 1.264911064 and -1.264911064.Subproblem 1
x + 6 = 1.264911064 Simplifying x + 6 = 1.264911064 Reorder the terms: 6 + x = 1.264911064 Solving 6 + x = 1.264911064 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 = 1.264911064 + -6 Combine like terms: 6 + -6 = 0 0 + x = 1.264911064 + -6 x = 1.264911064 + -6 Combine like terms: 1.264911064 + -6 = -4.735088936 x = -4.735088936 Simplifying x = -4.735088936Subproblem 2
x + 6 = -1.264911064 Simplifying x + 6 = -1.264911064 Reorder the terms: 6 + x = -1.264911064 Solving 6 + x = -1.264911064 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 = -1.264911064 + -6 Combine like terms: 6 + -6 = 0 0 + x = -1.264911064 + -6 x = -1.264911064 + -6 Combine like terms: -1.264911064 + -6 = -7.264911064 x = -7.264911064 Simplifying x = -7.264911064Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.735088936, -7.264911064}
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