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Simplifying (20 + -2x) + (40 + -2x) + (40 + -2x) + (40 + -2x)(20 + -2x) = 0 Remove parenthesis around (20 + -2x) 20 + -2x + (40 + -2x) + (40 + -2x) + (40 + -2x)(20 + -2x) = 0 Remove parenthesis around (40 + -2x) 20 + -2x + 40 + -2x + (40 + -2x) + (40 + -2x)(20 + -2x) = 0 Remove parenthesis around (40 + -2x) 20 + -2x + 40 + -2x + 40 + -2x + (40 + -2x)(20 + -2x) = 0 Multiply (40 + -2x) * (20 + -2x) 20 + -2x + 40 + -2x + 40 + -2x + (40(20 + -2x) + -2x * (20 + -2x)) = 0 20 + -2x + 40 + -2x + 40 + -2x + ((20 * 40 + -2x * 40) + -2x * (20 + -2x)) = 0 20 + -2x + 40 + -2x + 40 + -2x + ((800 + -80x) + -2x * (20 + -2x)) = 0 20 + -2x + 40 + -2x + 40 + -2x + (800 + -80x + (20 * -2x + -2x * -2x)) = 0 20 + -2x + 40 + -2x + 40 + -2x + (800 + -80x + (-40x + 4x2)) = 0 Combine like terms: -80x + -40x = -120x 20 + -2x + 40 + -2x + 40 + -2x + (800 + -120x + 4x2) = 0 Reorder the terms: 20 + 40 + 40 + 800 + -2x + -2x + -2x + -120x + 4x2 = 0 Combine like terms: 20 + 40 = 60 60 + 40 + 800 + -2x + -2x + -2x + -120x + 4x2 = 0 Combine like terms: 60 + 40 = 100 100 + 800 + -2x + -2x + -2x + -120x + 4x2 = 0 Combine like terms: 100 + 800 = 900 900 + -2x + -2x + -2x + -120x + 4x2 = 0 Combine like terms: -2x + -2x = -4x 900 + -4x + -2x + -120x + 4x2 = 0 Combine like terms: -4x + -2x = -6x 900 + -6x + -120x + 4x2 = 0 Combine like terms: -6x + -120x = -126x 900 + -126x + 4x2 = 0 Solving 900 + -126x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(450 + -63x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(450 + -63x + 2x2)' equal to zero and attempt to solve: Simplifying 450 + -63x + 2x2 = 0 Solving 450 + -63x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 225 + -31.5x + x2 = 0 Move the constant term to the right: Add '-225' to each side of the equation. 225 + -31.5x + -225 + x2 = 0 + -225 Reorder the terms: 225 + -225 + -31.5x + x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -31.5x + x2 = 0 + -225 -31.5x + x2 = 0 + -225 Combine like terms: 0 + -225 = -225 -31.5x + x2 = -225 The x term is -31.5x. Take half its coefficient (-15.75). Square it (248.0625) and add it to both sides. Add '248.0625' to each side of the equation. -31.5x + 248.0625 + x2 = -225 + 248.0625 Reorder the terms: 248.0625 + -31.5x + x2 = -225 + 248.0625 Combine like terms: -225 + 248.0625 = 23.0625 248.0625 + -31.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + -15.75)(x + -15.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + -15.75) equal to 4.802343178 and -4.802343178.Subproblem 1
x + -15.75 = 4.802343178 Simplifying x + -15.75 = 4.802343178 Reorder the terms: -15.75 + x = 4.802343178 Solving -15.75 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.75' to each side of the equation. -15.75 + 15.75 + x = 4.802343178 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + x = 4.802343178 + 15.75 x = 4.802343178 + 15.75 Combine like terms: 4.802343178 + 15.75 = 20.552343178 x = 20.552343178 Simplifying x = 20.552343178Subproblem 2
x + -15.75 = -4.802343178 Simplifying x + -15.75 = -4.802343178 Reorder the terms: -15.75 + x = -4.802343178 Solving -15.75 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.75' to each side of the equation. -15.75 + 15.75 + x = -4.802343178 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + x = -4.802343178 + 15.75 x = -4.802343178 + 15.75 Combine like terms: -4.802343178 + 15.75 = 10.947656822 x = 10.947656822 Simplifying x = 10.947656822Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.552343178, 10.947656822}Solution
x = {20.552343178, 10.947656822}
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