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Simplifying 16x2 + -160x + 100 = 0 Reorder the terms: 100 + -160x + 16x2 = 0 Solving 100 + -160x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -40x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + -40x + 4x2)' equal to zero and attempt to solve: Simplifying 25 + -40x + 4x2 = 0 Solving 25 + -40x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + -10x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -10x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -10x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -10x + x2 = 0 + -6.25 -10x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -10x + x2 = -6.25 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -6.25 + 25 Reorder the terms: 25 + -10x + x2 = -6.25 + 25 Combine like terms: -6.25 + 25 = 18.75 25 + -10x + x2 = 18.75 Factor a perfect square on the left side: (x + -5)(x + -5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + -5) equal to 4.330127019 and -4.330127019.Subproblem 1
x + -5 = 4.330127019 Simplifying x + -5 = 4.330127019 Reorder the terms: -5 + x = 4.330127019 Solving -5 + x = 4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.330127019 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.330127019 + 5 x = 4.330127019 + 5 Combine like terms: 4.330127019 + 5 = 9.330127019 x = 9.330127019 Simplifying x = 9.330127019Subproblem 2
x + -5 = -4.330127019 Simplifying x + -5 = -4.330127019 Reorder the terms: -5 + x = -4.330127019 Solving -5 + x = -4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.330127019 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.330127019 + 5 x = -4.330127019 + 5 Combine like terms: -4.330127019 + 5 = 0.669872981 x = 0.669872981 Simplifying x = 0.669872981Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.330127019, 0.669872981}Solution
x = {9.330127019, 0.669872981}
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