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Simplifying -16x2 + 65x + 80 = 0 Reorder the terms: 80 + 65x + -16x2 = 0 Solving 80 + 65x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -5 + -4.0625x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.0625x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -4.0625x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.0625x + x2 = 0 + 5 -4.0625x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.0625x + x2 = 5 The x term is -4.0625x. Take half its coefficient (-2.03125). Square it (4.125976563) and add it to both sides. Add '4.125976563' to each side of the equation. -4.0625x + 4.125976563 + x2 = 5 + 4.125976563 Reorder the terms: 4.125976563 + -4.0625x + x2 = 5 + 4.125976563 Combine like terms: 5 + 4.125976563 = 9.125976563 4.125976563 + -4.0625x + x2 = 9.125976563 Factor a perfect square on the left side: (x + -2.03125)(x + -2.03125) = 9.125976563 Calculate the square root of the right side: 3.020923131 Break this problem into two subproblems by setting (x + -2.03125) equal to 3.020923131 and -3.020923131.Subproblem 1
x + -2.03125 = 3.020923131 Simplifying x + -2.03125 = 3.020923131 Reorder the terms: -2.03125 + x = 3.020923131 Solving -2.03125 + x = 3.020923131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.03125' to each side of the equation. -2.03125 + 2.03125 + x = 3.020923131 + 2.03125 Combine like terms: -2.03125 + 2.03125 = 0.00000 0.00000 + x = 3.020923131 + 2.03125 x = 3.020923131 + 2.03125 Combine like terms: 3.020923131 + 2.03125 = 5.052173131 x = 5.052173131 Simplifying x = 5.052173131Subproblem 2
x + -2.03125 = -3.020923131 Simplifying x + -2.03125 = -3.020923131 Reorder the terms: -2.03125 + x = -3.020923131 Solving -2.03125 + x = -3.020923131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.03125' to each side of the equation. -2.03125 + 2.03125 + x = -3.020923131 + 2.03125 Combine like terms: -2.03125 + 2.03125 = 0.00000 0.00000 + x = -3.020923131 + 2.03125 x = -3.020923131 + 2.03125 Combine like terms: -3.020923131 + 2.03125 = -0.989673131 x = -0.989673131 Simplifying x = -0.989673131Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.052173131, -0.989673131}
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