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Simplifying -16x2 + 50x + 160 = 0 Reorder the terms: 160 + 50x + -16x2 = 0 Solving 160 + 50x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(80 + 25x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(80 + 25x + -8x2)' equal to zero and attempt to solve: Simplifying 80 + 25x + -8x2 = 0 Solving 80 + 25x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -10 + -3.125x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -3.125x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -3.125x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3.125x + x2 = 0 + 10 -3.125x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -3.125x + x2 = 10 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 = 10 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 10 + 2.44140625 Combine like terms: 10 + 2.44140625 = 12.44140625 2.44140625 + -3.125x + x2 = 12.44140625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 12.44140625 Calculate the square root of the right side: 3.527237765 Break this problem into two subproblems by setting (x + -1.5625) equal to 3.527237765 and -3.527237765.Subproblem 1
x + -1.5625 = 3.527237765 Simplifying x + -1.5625 = 3.527237765 Reorder the terms: -1.5625 + x = 3.527237765 Solving -1.5625 + x = 3.527237765 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 = 3.527237765 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 3.527237765 + 1.5625 x = 3.527237765 + 1.5625 Combine like terms: 3.527237765 + 1.5625 = 5.089737765 x = 5.089737765 Simplifying x = 5.089737765Subproblem 2
x + -1.5625 = -3.527237765 Simplifying x + -1.5625 = -3.527237765 Reorder the terms: -1.5625 + x = -3.527237765 Solving -1.5625 + x = -3.527237765 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 = -3.527237765 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -3.527237765 + 1.5625 x = -3.527237765 + 1.5625 Combine like terms: -3.527237765 + 1.5625 = -1.964737765 x = -1.964737765 Simplifying x = -1.964737765Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.089737765, -1.964737765}Solution
x = {5.089737765, -1.964737765}
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