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Simplifying 0 = 2x2 + -24x + -81 Reorder the terms: 0 = -81 + -24x + 2x2 Solving 0 = -81 + -24x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 81 = 81 81 + 24x + -2x2 = -81 + -24x + 2x2 + 81 + 24x + -2x2 Reorder the terms: 81 + 24x + -2x2 = -81 + 81 + -24x + 24x + 2x2 + -2x2 Combine like terms: -81 + 81 = 0 81 + 24x + -2x2 = 0 + -24x + 24x + 2x2 + -2x2 81 + 24x + -2x2 = -24x + 24x + 2x2 + -2x2 Combine like terms: -24x + 24x = 0 81 + 24x + -2x2 = 0 + 2x2 + -2x2 81 + 24x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 81 + 24x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -40.5 + -12x + x2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + -12x + 40.5 + x2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + -12x + x2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + -12x + x2 = 0 + 40.5 -12x + x2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 -12x + x2 = 40.5 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 = 40.5 + 36 Reorder the terms: 36 + -12x + x2 = 40.5 + 36 Combine like terms: 40.5 + 36 = 76.5 36 + -12x + x2 = 76.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 76.5 Calculate the square root of the right side: 8.746427842 Break this problem into two subproblems by setting (x + -6) equal to 8.746427842 and -8.746427842.Subproblem 1
x + -6 = 8.746427842 Simplifying x + -6 = 8.746427842 Reorder the terms: -6 + x = 8.746427842 Solving -6 + x = 8.746427842 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 = 8.746427842 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.746427842 + 6 x = 8.746427842 + 6 Combine like terms: 8.746427842 + 6 = 14.746427842 x = 14.746427842 Simplifying x = 14.746427842Subproblem 2
x + -6 = -8.746427842 Simplifying x + -6 = -8.746427842 Reorder the terms: -6 + x = -8.746427842 Solving -6 + x = -8.746427842 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 = -8.746427842 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.746427842 + 6 x = -8.746427842 + 6 Combine like terms: -8.746427842 + 6 = -2.746427842 x = -2.746427842 Simplifying x = -2.746427842Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.746427842, -2.746427842}
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