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Simplifying -4x2 + 16x + 81 = 0 Reorder the terms: 81 + 16x + -4x2 = 0 Solving 81 + 16x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -20.25 + -4x + x2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + -4x + 20.25 + x2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + -4x + x2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + -4x + x2 = 0 + 20.25 -4x + x2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 -4x + x2 = 20.25 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 20.25 + 4 Reorder the terms: 4 + -4x + x2 = 20.25 + 4 Combine like terms: 20.25 + 4 = 24.25 4 + -4x + x2 = 24.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + -2) equal to 4.924428901 and -4.924428901.Subproblem 1
x + -2 = 4.924428901 Simplifying x + -2 = 4.924428901 Reorder the terms: -2 + x = 4.924428901 Solving -2 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.924428901 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.924428901 + 2 x = 4.924428901 + 2 Combine like terms: 4.924428901 + 2 = 6.924428901 x = 6.924428901 Simplifying x = 6.924428901Subproblem 2
x + -2 = -4.924428901 Simplifying x + -2 = -4.924428901 Reorder the terms: -2 + x = -4.924428901 Solving -2 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.924428901 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.924428901 + 2 x = -4.924428901 + 2 Combine like terms: -4.924428901 + 2 = -2.924428901 x = -2.924428901 Simplifying x = -2.924428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.924428901, -2.924428901}
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