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Simplifying 0 = -16x2 + 40x + 5 Reorder the terms: 0 = 5 + 40x + -16x2 Solving 0 = 5 + 40x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -40x + 16x2 = 5 + 40x + -16x2 + -5 + -40x + 16x2 Reorder the terms: -5 + -40x + 16x2 = 5 + -5 + 40x + -40x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 -5 + -40x + 16x2 = 0 + 40x + -40x + -16x2 + 16x2 -5 + -40x + 16x2 = 40x + -40x + -16x2 + 16x2 Combine like terms: 40x + -40x = 0 -5 + -40x + 16x2 = 0 + -16x2 + 16x2 -5 + -40x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -40x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -2.5x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -2.5x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -2.5x + x2 = 0 + 0.3125 -2.5x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -2.5x + x2 = 0.3125 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 0.3125 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.3125 + 1.5625 Combine like terms: 0.3125 + 1.5625 = 1.875 1.5625 + -2.5x + x2 = 1.875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.875 Calculate the square root of the right side: 1.369306394 Break this problem into two subproblems by setting (x + -1.25) equal to 1.369306394 and -1.369306394.Subproblem 1
x + -1.25 = 1.369306394 Simplifying x + -1.25 = 1.369306394 Reorder the terms: -1.25 + x = 1.369306394 Solving -1.25 + x = 1.369306394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.369306394 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.369306394 + 1.25 x = 1.369306394 + 1.25 Combine like terms: 1.369306394 + 1.25 = 2.619306394 x = 2.619306394 Simplifying x = 2.619306394Subproblem 2
x + -1.25 = -1.369306394 Simplifying x + -1.25 = -1.369306394 Reorder the terms: -1.25 + x = -1.369306394 Solving -1.25 + x = -1.369306394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.369306394 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.369306394 + 1.25 x = -1.369306394 + 1.25 Combine like terms: -1.369306394 + 1.25 = -0.119306394 x = -0.119306394 Simplifying x = -0.119306394Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.619306394, -0.119306394}
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