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Simplifying -4x2 + 188 = 80x Reorder the terms: 188 + -4x2 = 80x Solving 188 + -4x2 = 80x Solving for variable 'x'. Reorder the terms: 188 + -80x + -4x2 = 80x + -80x Combine like terms: 80x + -80x = 0 188 + -80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(47 + -20x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(47 + -20x + -1x2)' equal to zero and attempt to solve: Simplifying 47 + -20x + -1x2 = 0 Solving 47 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -47 + 20x + x2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + 20x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + 20x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 20x + x2 = 0 + 47 20x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 20x + x2 = 47 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 = 47 + 100 Reorder the terms: 100 + 20x + x2 = 47 + 100 Combine like terms: 47 + 100 = 147 100 + 20x + x2 = 147 Factor a perfect square on the left side: (x + 10)(x + 10) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (x + 10) equal to 12.124355653 and -12.124355653.Subproblem 1
x + 10 = 12.124355653 Simplifying x + 10 = 12.124355653 Reorder the terms: 10 + x = 12.124355653 Solving 10 + x = 12.124355653 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 = 12.124355653 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.124355653 + -10 x = 12.124355653 + -10 Combine like terms: 12.124355653 + -10 = 2.124355653 x = 2.124355653 Simplifying x = 2.124355653Subproblem 2
x + 10 = -12.124355653 Simplifying x + 10 = -12.124355653 Reorder the terms: 10 + x = -12.124355653 Solving 10 + x = -12.124355653 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 = -12.124355653 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.124355653 + -10 x = -12.124355653 + -10 Combine like terms: -12.124355653 + -10 = -22.124355653 x = -22.124355653 Simplifying x = -22.124355653Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.124355653, -22.124355653}Solution
x = {2.124355653, -22.124355653}
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