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Simplifying -16x2 + 50x + 100 = 0 Reorder the terms: 100 + 50x + -16x2 = 0 Solving 100 + 50x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 25x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + 25x + -8x2)' equal to zero and attempt to solve: Simplifying 50 + 25x + -8x2 = 0 Solving 50 + 25x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -6.25 + -3.125x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -3.125x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -3.125x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -3.125x + x2 = 0 + 6.25 -3.125x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -3.125x + x2 = 6.25 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 6.25 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 6.25 + 2.44140625 Combine like terms: 6.25 + 2.44140625 = 8.69140625 2.44140625 + -3.125x + x2 = 8.69140625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 8.69140625 Calculate the square root of the right side: 2.948119104 Break this problem into two subproblems by setting (x + -1.5625) equal to 2.948119104 and -2.948119104.Subproblem 1
x + -1.5625 = 2.948119104 Simplifying x + -1.5625 = 2.948119104 Reorder the terms: -1.5625 + x = 2.948119104 Solving -1.5625 + x = 2.948119104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 2.948119104 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 2.948119104 + 1.5625 x = 2.948119104 + 1.5625 Combine like terms: 2.948119104 + 1.5625 = 4.510619104 x = 4.510619104 Simplifying x = 4.510619104Subproblem 2
x + -1.5625 = -2.948119104 Simplifying x + -1.5625 = -2.948119104 Reorder the terms: -1.5625 + x = -2.948119104 Solving -1.5625 + x = -2.948119104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -2.948119104 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -2.948119104 + 1.5625 x = -2.948119104 + 1.5625 Combine like terms: -2.948119104 + 1.5625 = -1.385619104 x = -1.385619104 Simplifying x = -1.385619104Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.510619104, -1.385619104}Solution
x = {4.510619104, -1.385619104}
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