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Simplifying -16x2 + 160x + 30 = 0 Reorder the terms: 30 + 160x + -16x2 = 0 Solving 30 + 160x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 80x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 80x + -8x2)' equal to zero and attempt to solve: Simplifying 15 + 80x + -8x2 = 0 Solving 15 + 80x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + -10x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -10x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -10x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -10x + x2 = 0 + 1.875 -10x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -10x + x2 = 1.875 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 = 1.875 + 25 Reorder the terms: 25 + -10x + x2 = 1.875 + 25 Combine like terms: 1.875 + 25 = 26.875 25 + -10x + x2 = 26.875 Factor a perfect square on the left side: (x + -5)(x + -5) = 26.875 Calculate the square root of the right side: 5.184110338 Break this problem into two subproblems by setting (x + -5) equal to 5.184110338 and -5.184110338.Subproblem 1
x + -5 = 5.184110338 Simplifying x + -5 = 5.184110338 Reorder the terms: -5 + x = 5.184110338 Solving -5 + x = 5.184110338 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 = 5.184110338 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.184110338 + 5 x = 5.184110338 + 5 Combine like terms: 5.184110338 + 5 = 10.184110338 x = 10.184110338 Simplifying x = 10.184110338Subproblem 2
x + -5 = -5.184110338 Simplifying x + -5 = -5.184110338 Reorder the terms: -5 + x = -5.184110338 Solving -5 + x = -5.184110338 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 = -5.184110338 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.184110338 + 5 x = -5.184110338 + 5 Combine like terms: -5.184110338 + 5 = -0.184110338 x = -0.184110338 Simplifying x = -0.184110338Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.184110338, -0.184110338}Solution
x = {10.184110338, -0.184110338}
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