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Simplifying 9x2 + 3x + 5 = 60 Reorder the terms: 5 + 3x + 9x2 = 60 Solving 5 + 3x + 9x2 = 60 Solving for variable 'x'. Reorder the terms: 5 + -60 + 3x + 9x2 = 60 + -60 Combine like terms: 5 + -60 = -55 -55 + 3x + 9x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -55 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.111111111 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '6.111111111' to each side of the equation. -6.111111111 + 0.3333333333x + 6.111111111 + x2 = 0 + 6.111111111 Reorder the terms: -6.111111111 + 6.111111111 + 0.3333333333x + x2 = 0 + 6.111111111 Combine like terms: -6.111111111 + 6.111111111 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + 6.111111111 0.3333333333x + x2 = 0 + 6.111111111 Combine like terms: 0 + 6.111111111 = 6.111111111 0.3333333333x + x2 = 6.111111111 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 6.111111111 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 6.111111111 + 0.02777777779 Combine like terms: 6.111111111 + 0.02777777779 = 6.13888888879 0.02777777779 + 0.3333333333x + x2 = 6.13888888879 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 6.13888888879 Calculate the square root of the right side: 2.477678125 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 2.477678125 and -2.477678125.Subproblem 1
x + 0.1666666667 = 2.477678125 Simplifying x + 0.1666666667 = 2.477678125 Reorder the terms: 0.1666666667 + x = 2.477678125 Solving 0.1666666667 + x = 2.477678125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 2.477678125 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 2.477678125 + -0.1666666667 x = 2.477678125 + -0.1666666667 Combine like terms: 2.477678125 + -0.1666666667 = 2.3110114583 x = 2.3110114583 Simplifying x = 2.3110114583Subproblem 2
x + 0.1666666667 = -2.477678125 Simplifying x + 0.1666666667 = -2.477678125 Reorder the terms: 0.1666666667 + x = -2.477678125 Solving 0.1666666667 + x = -2.477678125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -2.477678125 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -2.477678125 + -0.1666666667 x = -2.477678125 + -0.1666666667 Combine like terms: -2.477678125 + -0.1666666667 = -2.6443447917 x = -2.6443447917 Simplifying x = -2.6443447917Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3110114583, -2.6443447917}
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