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Simplifying 16x2 + -160x + 308 = 0 Reorder the terms: 308 + -160x + 16x2 = 0 Solving 308 + -160x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(77 + -40x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(77 + -40x + 4x2)' equal to zero and attempt to solve: Simplifying 77 + -40x + 4x2 = 0 Solving 77 + -40x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 19.25 + -10x + x2 = 0 Move the constant term to the right: Add '-19.25' to each side of the equation. 19.25 + -10x + -19.25 + x2 = 0 + -19.25 Reorder the terms: 19.25 + -19.25 + -10x + x2 = 0 + -19.25 Combine like terms: 19.25 + -19.25 = 0.00 0.00 + -10x + x2 = 0 + -19.25 -10x + x2 = 0 + -19.25 Combine like terms: 0 + -19.25 = -19.25 -10x + x2 = -19.25 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 = -19.25 + 25 Reorder the terms: 25 + -10x + x2 = -19.25 + 25 Combine like terms: -19.25 + 25 = 5.75 25 + -10x + x2 = 5.75 Factor a perfect square on the left side: (x + -5)(x + -5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + -5) equal to 2.397915762 and -2.397915762.Subproblem 1
x + -5 = 2.397915762 Simplifying x + -5 = 2.397915762 Reorder the terms: -5 + x = 2.397915762 Solving -5 + x = 2.397915762 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 = 2.397915762 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.397915762 + 5 x = 2.397915762 + 5 Combine like terms: 2.397915762 + 5 = 7.397915762 x = 7.397915762 Simplifying x = 7.397915762Subproblem 2
x + -5 = -2.397915762 Simplifying x + -5 = -2.397915762 Reorder the terms: -5 + x = -2.397915762 Solving -5 + x = -2.397915762 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 = -2.397915762 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.397915762 + 5 x = -2.397915762 + 5 Combine like terms: -2.397915762 + 5 = 2.602084238 x = 2.602084238 Simplifying x = 2.602084238Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.397915762, 2.602084238}Solution
x = {7.397915762, 2.602084238}
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