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Simplifying (30 + -2x)(20 + -2x) = 400 Multiply (30 + -2x) * (20 + -2x) (30(20 + -2x) + -2x * (20 + -2x)) = 400 ((20 * 30 + -2x * 30) + -2x * (20 + -2x)) = 400 ((600 + -60x) + -2x * (20 + -2x)) = 400 (600 + -60x + (20 * -2x + -2x * -2x)) = 400 (600 + -60x + (-40x + 4x2)) = 400 Combine like terms: -60x + -40x = -100x (600 + -100x + 4x2) = 400 Solving 600 + -100x + 4x2 = 400 Solving for variable 'x'. Reorder the terms: 600 + -400 + -100x + 4x2 = 400 + -400 Combine like terms: 600 + -400 = 200 200 + -100x + 4x2 = 400 + -400 Combine like terms: 400 + -400 = 0 200 + -100x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(50 + -25x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(50 + -25x + x2)' equal to zero and attempt to solve: Simplifying 50 + -25x + x2 = 0 Solving 50 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -25x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -25x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -25x + x2 = 0 + -50 -25x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -25x + x2 = -50 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -50 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -50 + 156.25 Combine like terms: -50 + 156.25 = 106.25 156.25 + -25x + x2 = 106.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + -12.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + -12.5 = 10.307764064 Simplifying x + -12.5 = 10.307764064 Reorder the terms: -12.5 + x = 10.307764064 Solving -12.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 10.307764064 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.307764064 + 12.5 x = 10.307764064 + 12.5 Combine like terms: 10.307764064 + 12.5 = 22.807764064 x = 22.807764064 Simplifying x = 22.807764064Subproblem 2
x + -12.5 = -10.307764064 Simplifying x + -12.5 = -10.307764064 Reorder the terms: -12.5 + x = -10.307764064 Solving -12.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -10.307764064 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.307764064 + 12.5 x = -10.307764064 + 12.5 Combine like terms: -10.307764064 + 12.5 = 2.192235936 x = 2.192235936 Simplifying x = 2.192235936Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.807764064, 2.192235936}Solution
x = {22.807764064, 2.192235936}
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