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Simplifying 100 = -16x2 + 98x + 5 Reorder the terms: 100 = 5 + 98x + -16x2 Solving 100 = 5 + 98x + -16x2 Solving for variable 'x'. Combine like terms: 100 + -5 = 95 95 + -98x + 16x2 = 5 + 98x + -16x2 + -5 + -98x + 16x2 Reorder the terms: 95 + -98x + 16x2 = 5 + -5 + 98x + -98x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 95 + -98x + 16x2 = 0 + 98x + -98x + -16x2 + 16x2 95 + -98x + 16x2 = 98x + -98x + -16x2 + 16x2 Combine like terms: 98x + -98x = 0 95 + -98x + 16x2 = 0 + -16x2 + 16x2 95 + -98x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 95 + -98x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.9375 + -6.125x + x2 = 0 Move the constant term to the right: Add '-5.9375' to each side of the equation. 5.9375 + -6.125x + -5.9375 + x2 = 0 + -5.9375 Reorder the terms: 5.9375 + -5.9375 + -6.125x + x2 = 0 + -5.9375 Combine like terms: 5.9375 + -5.9375 = 0.0000 0.0000 + -6.125x + x2 = 0 + -5.9375 -6.125x + x2 = 0 + -5.9375 Combine like terms: 0 + -5.9375 = -5.9375 -6.125x + x2 = -5.9375 The x term is -6.125x. Take half its coefficient (-3.0625). Square it (9.37890625) and add it to both sides. Add '9.37890625' to each side of the equation. -6.125x + 9.37890625 + x2 = -5.9375 + 9.37890625 Reorder the terms: 9.37890625 + -6.125x + x2 = -5.9375 + 9.37890625 Combine like terms: -5.9375 + 9.37890625 = 3.44140625 9.37890625 + -6.125x + x2 = 3.44140625 Factor a perfect square on the left side: (x + -3.0625)(x + -3.0625) = 3.44140625 Calculate the square root of the right side: 1.85510276 Break this problem into two subproblems by setting (x + -3.0625) equal to 1.85510276 and -1.85510276.Subproblem 1
x + -3.0625 = 1.85510276 Simplifying x + -3.0625 = 1.85510276 Reorder the terms: -3.0625 + x = 1.85510276 Solving -3.0625 + x = 1.85510276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + x = 1.85510276 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + x = 1.85510276 + 3.0625 x = 1.85510276 + 3.0625 Combine like terms: 1.85510276 + 3.0625 = 4.91760276 x = 4.91760276 Simplifying x = 4.91760276Subproblem 2
x + -3.0625 = -1.85510276 Simplifying x + -3.0625 = -1.85510276 Reorder the terms: -3.0625 + x = -1.85510276 Solving -3.0625 + x = -1.85510276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + x = -1.85510276 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + x = -1.85510276 + 3.0625 x = -1.85510276 + 3.0625 Combine like terms: -1.85510276 + 3.0625 = 1.20739724 x = 1.20739724 Simplifying x = 1.20739724Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.91760276, 1.20739724}
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