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Simplifying -16x2 + 80x + 45 = 0 Reorder the terms: 45 + 80x + -16x2 = 0 Solving 45 + 80x + -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'. -2.8125 + -5x + x2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + -5x + 2.8125 + x2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + -5x + x2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + -5x + x2 = 0 + 2.8125 -5x + x2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 -5x + x2 = 2.8125 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 2.8125 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 2.8125 + 6.25 Combine like terms: 2.8125 + 6.25 = 9.0625 6.25 + -5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -2.5) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -2.5 = 3.010398645 Simplifying x + -2.5 = 3.010398645 Reorder the terms: -2.5 + x = 3.010398645 Solving -2.5 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.010398645 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.010398645 + 2.5 x = 3.010398645 + 2.5 Combine like terms: 3.010398645 + 2.5 = 5.510398645 x = 5.510398645 Simplifying x = 5.510398645Subproblem 2
x + -2.5 = -3.010398645 Simplifying x + -2.5 = -3.010398645 Reorder the terms: -2.5 + x = -3.010398645 Solving -2.5 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.010398645 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.010398645 + 2.5 x = -3.010398645 + 2.5 Combine like terms: -3.010398645 + 2.5 = -0.510398645 x = -0.510398645 Simplifying x = -0.510398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.510398645, -0.510398645}
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