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Simplifying 3x + (2x + 20)(4x + -20) = 180 Reorder the terms: 3x + (20 + 2x)(4x + -20) = 180 Reorder the terms: 3x + (20 + 2x)(-20 + 4x) = 180 Multiply (20 + 2x) * (-20 + 4x) 3x + (20(-20 + 4x) + 2x * (-20 + 4x)) = 180 3x + ((-20 * 20 + 4x * 20) + 2x * (-20 + 4x)) = 180 3x + ((-400 + 80x) + 2x * (-20 + 4x)) = 180 3x + (-400 + 80x + (-20 * 2x + 4x * 2x)) = 180 3x + (-400 + 80x + (-40x + 8x2)) = 180 Combine like terms: 80x + -40x = 40x 3x + (-400 + 40x + 8x2) = 180 Reorder the terms: -400 + 3x + 40x + 8x2 = 180 Combine like terms: 3x + 40x = 43x -400 + 43x + 8x2 = 180 Solving -400 + 43x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: -400 + -180 + 43x + 8x2 = 180 + -180 Combine like terms: -400 + -180 = -580 -580 + 43x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -580 + 43x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -72.5 + 5.375x + x2 = 0 Move the constant term to the right: Add '72.5' to each side of the equation. -72.5 + 5.375x + 72.5 + x2 = 0 + 72.5 Reorder the terms: -72.5 + 72.5 + 5.375x + x2 = 0 + 72.5 Combine like terms: -72.5 + 72.5 = 0.0 0.0 + 5.375x + x2 = 0 + 72.5 5.375x + x2 = 0 + 72.5 Combine like terms: 0 + 72.5 = 72.5 5.375x + x2 = 72.5 The x term is 5.375x. Take half its coefficient (2.6875). Square it (7.22265625) and add it to both sides. Add '7.22265625' to each side of the equation. 5.375x + 7.22265625 + x2 = 72.5 + 7.22265625 Reorder the terms: 7.22265625 + 5.375x + x2 = 72.5 + 7.22265625 Combine like terms: 72.5 + 7.22265625 = 79.72265625 7.22265625 + 5.375x + x2 = 79.72265625 Factor a perfect square on the left side: (x + 2.6875)(x + 2.6875) = 79.72265625 Calculate the square root of the right side: 8.928754462 Break this problem into two subproblems by setting (x + 2.6875) equal to 8.928754462 and -8.928754462.Subproblem 1
x + 2.6875 = 8.928754462 Simplifying x + 2.6875 = 8.928754462 Reorder the terms: 2.6875 + x = 8.928754462 Solving 2.6875 + x = 8.928754462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6875' to each side of the equation. 2.6875 + -2.6875 + x = 8.928754462 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + x = 8.928754462 + -2.6875 x = 8.928754462 + -2.6875 Combine like terms: 8.928754462 + -2.6875 = 6.241254462 x = 6.241254462 Simplifying x = 6.241254462Subproblem 2
x + 2.6875 = -8.928754462 Simplifying x + 2.6875 = -8.928754462 Reorder the terms: 2.6875 + x = -8.928754462 Solving 2.6875 + x = -8.928754462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6875' to each side of the equation. 2.6875 + -2.6875 + x = -8.928754462 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + x = -8.928754462 + -2.6875 x = -8.928754462 + -2.6875 Combine like terms: -8.928754462 + -2.6875 = -11.616254462 x = -11.616254462 Simplifying x = -11.616254462Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.241254462, -11.616254462}
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