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Simplifying 0 = 12x2 + -144x + 299 Reorder the terms: 0 = 299 + -144x + 12x2 Solving 0 = 299 + -144x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -299 = -299 -299 + 144x + -12x2 = 299 + -144x + 12x2 + -299 + 144x + -12x2 Reorder the terms: -299 + 144x + -12x2 = 299 + -299 + -144x + 144x + 12x2 + -12x2 Combine like terms: 299 + -299 = 0 -299 + 144x + -12x2 = 0 + -144x + 144x + 12x2 + -12x2 -299 + 144x + -12x2 = -144x + 144x + 12x2 + -12x2 Combine like terms: -144x + 144x = 0 -299 + 144x + -12x2 = 0 + 12x2 + -12x2 -299 + 144x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -299 + 144x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 24.91666667 + -12x + x2 = 0 Move the constant term to the right: Add '-24.91666667' to each side of the equation. 24.91666667 + -12x + -24.91666667 + x2 = 0 + -24.91666667 Reorder the terms: 24.91666667 + -24.91666667 + -12x + x2 = 0 + -24.91666667 Combine like terms: 24.91666667 + -24.91666667 = 0.00000000 0.00000000 + -12x + x2 = 0 + -24.91666667 -12x + x2 = 0 + -24.91666667 Combine like terms: 0 + -24.91666667 = -24.91666667 -12x + x2 = -24.91666667 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 = -24.91666667 + 36 Reorder the terms: 36 + -12x + x2 = -24.91666667 + 36 Combine like terms: -24.91666667 + 36 = 11.08333333 36 + -12x + x2 = 11.08333333 Factor a perfect square on the left side: (x + -6)(x + -6) = 11.08333333 Calculate the square root of the right side: 3.329164059 Break this problem into two subproblems by setting (x + -6) equal to 3.329164059 and -3.329164059.Subproblem 1
x + -6 = 3.329164059 Simplifying x + -6 = 3.329164059 Reorder the terms: -6 + x = 3.329164059 Solving -6 + x = 3.329164059 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 = 3.329164059 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.329164059 + 6 x = 3.329164059 + 6 Combine like terms: 3.329164059 + 6 = 9.329164059 x = 9.329164059 Simplifying x = 9.329164059Subproblem 2
x + -6 = -3.329164059 Simplifying x + -6 = -3.329164059 Reorder the terms: -6 + x = -3.329164059 Solving -6 + x = -3.329164059 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 = -3.329164059 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.329164059 + 6 x = -3.329164059 + 6 Combine like terms: -3.329164059 + 6 = 2.670835941 x = 2.670835941 Simplifying x = 2.670835941Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.329164059, 2.670835941}
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