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Simplifying 8x2 + -96x + 140 = 0 Reorder the terms: 140 + -96x + 8x2 = 0 Solving 140 + -96x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(35 + -24x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + -24x + 2x2)' equal to zero and attempt to solve: Simplifying 35 + -24x + 2x2 = 0 Solving 35 + -24x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 17.5 + -12x + x2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + -12x + -17.5 + x2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + -12x + x2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + -12x + x2 = 0 + -17.5 -12x + x2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 -12x + x2 = -17.5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -17.5 + 36 Reorder the terms: 36 + -12x + x2 = -17.5 + 36 Combine like terms: -17.5 + 36 = 18.5 36 + -12x + x2 = 18.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (x + -6) equal to 4.301162634 and -4.301162634.Subproblem 1
x + -6 = 4.301162634 Simplifying x + -6 = 4.301162634 Reorder the terms: -6 + x = 4.301162634 Solving -6 + x = 4.301162634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.301162634 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.301162634 + 6 x = 4.301162634 + 6 Combine like terms: 4.301162634 + 6 = 10.301162634 x = 10.301162634 Simplifying x = 10.301162634Subproblem 2
x + -6 = -4.301162634 Simplifying x + -6 = -4.301162634 Reorder the terms: -6 + x = -4.301162634 Solving -6 + x = -4.301162634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.301162634 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.301162634 + 6 x = -4.301162634 + 6 Combine like terms: -4.301162634 + 6 = 1.698837366 x = 1.698837366 Simplifying x = 1.698837366Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.301162634, 1.698837366}Solution
x = {10.301162634, 1.698837366}
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