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Simplifying 3x2 + 72x = 17084 Reorder the terms: 72x + 3x2 = 17084 Solving 72x + 3x2 = 17084 Solving for variable 'x'. Reorder the terms: -17084 + 72x + 3x2 = 17084 + -17084 Combine like terms: 17084 + -17084 = 0 -17084 + 72x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5694.666667 + 24x + x2 = 0 Move the constant term to the right: Add '5694.666667' to each side of the equation. -5694.666667 + 24x + 5694.666667 + x2 = 0 + 5694.666667 Reorder the terms: -5694.666667 + 5694.666667 + 24x + x2 = 0 + 5694.666667 Combine like terms: -5694.666667 + 5694.666667 = 0.000000 0.000000 + 24x + x2 = 0 + 5694.666667 24x + x2 = 0 + 5694.666667 Combine like terms: 0 + 5694.666667 = 5694.666667 24x + x2 = 5694.666667 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 5694.666667 + 144 Reorder the terms: 144 + 24x + x2 = 5694.666667 + 144 Combine like terms: 5694.666667 + 144 = 5838.666667 144 + 24x + x2 = 5838.666667 Factor a perfect square on the left side: (x + 12)(x + 12) = 5838.666667 Calculate the square root of the right side: 76.41116847 Break this problem into two subproblems by setting (x + 12) equal to 76.41116847 and -76.41116847.Subproblem 1
x + 12 = 76.41116847 Simplifying x + 12 = 76.41116847 Reorder the terms: 12 + x = 76.41116847 Solving 12 + x = 76.41116847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 76.41116847 + -12 Combine like terms: 12 + -12 = 0 0 + x = 76.41116847 + -12 x = 76.41116847 + -12 Combine like terms: 76.41116847 + -12 = 64.41116847 x = 64.41116847 Simplifying x = 64.41116847Subproblem 2
x + 12 = -76.41116847 Simplifying x + 12 = -76.41116847 Reorder the terms: 12 + x = -76.41116847 Solving 12 + x = -76.41116847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -76.41116847 + -12 Combine like terms: 12 + -12 = 0 0 + x = -76.41116847 + -12 x = -76.41116847 + -12 Combine like terms: -76.41116847 + -12 = -88.41116847 x = -88.41116847 Simplifying x = -88.41116847Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.41116847, -88.41116847}
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