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Simplifying (47 + -2x)(23 + -2x) = 595 Multiply (47 + -2x) * (23 + -2x) (47(23 + -2x) + -2x * (23 + -2x)) = 595 ((23 * 47 + -2x * 47) + -2x * (23 + -2x)) = 595 ((1081 + -94x) + -2x * (23 + -2x)) = 595 (1081 + -94x + (23 * -2x + -2x * -2x)) = 595 (1081 + -94x + (-46x + 4x2)) = 595 Combine like terms: -94x + -46x = -140x (1081 + -140x + 4x2) = 595 Solving 1081 + -140x + 4x2 = 595 Solving for variable 'x'. Reorder the terms: 1081 + -595 + -140x + 4x2 = 595 + -595 Combine like terms: 1081 + -595 = 486 486 + -140x + 4x2 = 595 + -595 Combine like terms: 595 + -595 = 0 486 + -140x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(243 + -70x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(243 + -70x + 2x2)' equal to zero and attempt to solve: Simplifying 243 + -70x + 2x2 = 0 Solving 243 + -70x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 121.5 + -35x + x2 = 0 Move the constant term to the right: Add '-121.5' to each side of the equation. 121.5 + -35x + -121.5 + x2 = 0 + -121.5 Reorder the terms: 121.5 + -121.5 + -35x + x2 = 0 + -121.5 Combine like terms: 121.5 + -121.5 = 0.0 0.0 + -35x + x2 = 0 + -121.5 -35x + x2 = 0 + -121.5 Combine like terms: 0 + -121.5 = -121.5 -35x + x2 = -121.5 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -121.5 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -121.5 + 306.25 Combine like terms: -121.5 + 306.25 = 184.75 306.25 + -35x + x2 = 184.75 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 184.75 Calculate the square root of the right side: 13.592277219 Break this problem into two subproblems by setting (x + -17.5) equal to 13.592277219 and -13.592277219.Subproblem 1
x + -17.5 = 13.592277219 Simplifying x + -17.5 = 13.592277219 Reorder the terms: -17.5 + x = 13.592277219 Solving -17.5 + x = 13.592277219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 13.592277219 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 13.592277219 + 17.5 x = 13.592277219 + 17.5 Combine like terms: 13.592277219 + 17.5 = 31.092277219 x = 31.092277219 Simplifying x = 31.092277219Subproblem 2
x + -17.5 = -13.592277219 Simplifying x + -17.5 = -13.592277219 Reorder the terms: -17.5 + x = -13.592277219 Solving -17.5 + x = -13.592277219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -13.592277219 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -13.592277219 + 17.5 x = -13.592277219 + 17.5 Combine like terms: -13.592277219 + 17.5 = 3.907722781 x = 3.907722781 Simplifying x = 3.907722781Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.092277219, 3.907722781}Solution
x = {31.092277219, 3.907722781}
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