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Simplifying 2x2 + 48x + -81 = 0 Reorder the terms: -81 + 48x + 2x2 = 0 Solving -81 + 48x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40.5 + 24x + x2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + 24x + 40.5 + x2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + 24x + x2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + 24x + x2 = 0 + 40.5 24x + x2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 24x + x2 = 40.5 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 = 40.5 + 144 Reorder the terms: 144 + 24x + x2 = 40.5 + 144 Combine like terms: 40.5 + 144 = 184.5 144 + 24x + x2 = 184.5 Factor a perfect square on the left side: (x + 12)(x + 12) = 184.5 Calculate the square root of the right side: 13.583077707 Break this problem into two subproblems by setting (x + 12) equal to 13.583077707 and -13.583077707.Subproblem 1
x + 12 = 13.583077707 Simplifying x + 12 = 13.583077707 Reorder the terms: 12 + x = 13.583077707 Solving 12 + x = 13.583077707 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 = 13.583077707 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.583077707 + -12 x = 13.583077707 + -12 Combine like terms: 13.583077707 + -12 = 1.583077707 x = 1.583077707 Simplifying x = 1.583077707Subproblem 2
x + 12 = -13.583077707 Simplifying x + 12 = -13.583077707 Reorder the terms: 12 + x = -13.583077707 Solving 12 + x = -13.583077707 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 = -13.583077707 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.583077707 + -12 x = -13.583077707 + -12 Combine like terms: -13.583077707 + -12 = -25.583077707 x = -25.583077707 Simplifying x = -25.583077707Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.583077707, -25.583077707}
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