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Simplifying 0 = -16x2 + 100x + 5 Reorder the terms: 0 = 5 + 100x + -16x2 Solving 0 = 5 + 100x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -100x + 16x2 = 5 + 100x + -16x2 + -5 + -100x + 16x2 Reorder the terms: -5 + -100x + 16x2 = 5 + -5 + 100x + -100x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 -5 + -100x + 16x2 = 0 + 100x + -100x + -16x2 + 16x2 -5 + -100x + 16x2 = 100x + -100x + -16x2 + 16x2 Combine like terms: 100x + -100x = 0 -5 + -100x + 16x2 = 0 + -16x2 + 16x2 -5 + -100x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -100x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -6.25x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -6.25x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -6.25x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -6.25x + x2 = 0 + 0.3125 -6.25x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -6.25x + x2 = 0.3125 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 0.3125 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 0.3125 + 9.765625 Combine like terms: 0.3125 + 9.765625 = 10.078125 9.765625 + -6.25x + x2 = 10.078125 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 10.078125 Calculate the square root of the right side: 3.174606275 Break this problem into two subproblems by setting (x + -3.125) equal to 3.174606275 and -3.174606275.Subproblem 1
x + -3.125 = 3.174606275 Simplifying x + -3.125 = 3.174606275 Reorder the terms: -3.125 + x = 3.174606275 Solving -3.125 + x = 3.174606275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.174606275 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.174606275 + 3.125 x = 3.174606275 + 3.125 Combine like terms: 3.174606275 + 3.125 = 6.299606275 x = 6.299606275 Simplifying x = 6.299606275Subproblem 2
x + -3.125 = -3.174606275 Simplifying x + -3.125 = -3.174606275 Reorder the terms: -3.125 + x = -3.174606275 Solving -3.125 + x = -3.174606275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.174606275 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.174606275 + 3.125 x = -3.174606275 + 3.125 Combine like terms: -3.174606275 + 3.125 = -0.049606275 x = -0.049606275 Simplifying x = -0.049606275Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.299606275, -0.049606275}
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