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Simplifying 3x2 + x = 305 Reorder the terms: x + 3x2 = 305 Solving x + 3x2 = 305 Solving for variable 'x'. Reorder the terms: -305 + x + 3x2 = 305 + -305 Combine like terms: 305 + -305 = 0 -305 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -101.6666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '101.6666667' to each side of the equation. -101.6666667 + 0.3333333333x + 101.6666667 + x2 = 0 + 101.6666667 Reorder the terms: -101.6666667 + 101.6666667 + 0.3333333333x + x2 = 0 + 101.6666667 Combine like terms: -101.6666667 + 101.6666667 = 0.0000000 0.0000000 + 0.3333333333x + x2 = 0 + 101.6666667 0.3333333333x + x2 = 0 + 101.6666667 Combine like terms: 0 + 101.6666667 = 101.6666667 0.3333333333x + x2 = 101.6666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 101.6666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 101.6666667 + 0.25 Combine like terms: 101.6666667 + 0.25 = 101.9166667 0.25 + 0.3333333333x + x2 = 101.9166667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 101.9166667 Calculate the square root of the right side: 10.095378482 Break this problem into two subproblems by setting (x + 0.5) equal to 10.095378482 and -10.095378482.Subproblem 1
x + 0.5 = 10.095378482 Simplifying x + 0.5 = 10.095378482 Reorder the terms: 0.5 + x = 10.095378482 Solving 0.5 + x = 10.095378482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 10.095378482 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.095378482 + -0.5 x = 10.095378482 + -0.5 Combine like terms: 10.095378482 + -0.5 = 9.595378482 x = 9.595378482 Simplifying x = 9.595378482Subproblem 2
x + 0.5 = -10.095378482 Simplifying x + 0.5 = -10.095378482 Reorder the terms: 0.5 + x = -10.095378482 Solving 0.5 + x = -10.095378482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -10.095378482 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.095378482 + -0.5 x = -10.095378482 + -0.5 Combine like terms: -10.095378482 + -0.5 = -10.595378482 x = -10.595378482 Simplifying x = -10.595378482Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.595378482, -10.595378482}
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