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Simplifying -16x2 + 110x + 160 = 0 Reorder the terms: 160 + 110x + -16x2 = 0 Solving 160 + 110x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(80 + 55x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(80 + 55x + -8x2)' equal to zero and attempt to solve: Simplifying 80 + 55x + -8x2 = 0 Solving 80 + 55x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -10 + -6.875x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -6.875x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -6.875x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6.875x + x2 = 0 + 10 -6.875x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6.875x + x2 = 10 The x term is -6.875x. Take half its coefficient (-3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. -6.875x + 11.81640625 + x2 = 10 + 11.81640625 Reorder the terms: 11.81640625 + -6.875x + x2 = 10 + 11.81640625 Combine like terms: 10 + 11.81640625 = 21.81640625 11.81640625 + -6.875x + x2 = 21.81640625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 21.81640625 Calculate the square root of the right side: 4.670803598 Break this problem into two subproblems by setting (x + -3.4375) equal to 4.670803598 and -4.670803598.Subproblem 1
x + -3.4375 = 4.670803598 Simplifying x + -3.4375 = 4.670803598 Reorder the terms: -3.4375 + x = 4.670803598 Solving -3.4375 + x = 4.670803598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = 4.670803598 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 4.670803598 + 3.4375 x = 4.670803598 + 3.4375 Combine like terms: 4.670803598 + 3.4375 = 8.108303598 x = 8.108303598 Simplifying x = 8.108303598Subproblem 2
x + -3.4375 = -4.670803598 Simplifying x + -3.4375 = -4.670803598 Reorder the terms: -3.4375 + x = -4.670803598 Solving -3.4375 + x = -4.670803598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = -4.670803598 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -4.670803598 + 3.4375 x = -4.670803598 + 3.4375 Combine like terms: -4.670803598 + 3.4375 = -1.233303598 x = -1.233303598 Simplifying x = -1.233303598Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.108303598, -1.233303598}Solution
x = {8.108303598, -1.233303598}
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