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Simplifying 80x + -4x2 = 8 Solving 80x + -4x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 80x + -4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 20x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 20x + -1x2 = 0 Solving -2 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -20x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -20x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -20x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -20x + x2 = 0 + -2 -20x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -20x + x2 = -2 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -2 + 100 Reorder the terms: 100 + -20x + x2 = -2 + 100 Combine like terms: -2 + 100 = 98 100 + -20x + x2 = 98 Factor a perfect square on the left side: (x + -10)(x + -10) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -10) equal to 9.899494937 and -9.899494937.Subproblem 1
x + -10 = 9.899494937 Simplifying x + -10 = 9.899494937 Reorder the terms: -10 + x = 9.899494937 Solving -10 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.899494937 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.899494937 + 10 x = 9.899494937 + 10 Combine like terms: 9.899494937 + 10 = 19.899494937 x = 19.899494937 Simplifying x = 19.899494937Subproblem 2
x + -10 = -9.899494937 Simplifying x + -10 = -9.899494937 Reorder the terms: -10 + x = -9.899494937 Solving -10 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.899494937 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.899494937 + 10 x = -9.899494937 + 10 Combine like terms: -9.899494937 + 10 = 0.100505063 x = 0.100505063 Simplifying x = 0.100505063Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.899494937, 0.100505063}Solution
x = {19.899494937, 0.100505063}
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