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Simplifying x2 + -20x + 38 = 7x + 2 Reorder the terms: 38 + -20x + x2 = 7x + 2 Reorder the terms: 38 + -20x + x2 = 2 + 7x Solving 38 + -20x + x2 = 2 + 7x Solving for variable 'x'. Reorder the terms: 38 + -2 + -20x + -7x + x2 = 2 + 7x + -2 + -7x Combine like terms: 38 + -2 = 36 36 + -20x + -7x + x2 = 2 + 7x + -2 + -7x Combine like terms: -20x + -7x = -27x 36 + -27x + x2 = 2 + 7x + -2 + -7x Reorder the terms: 36 + -27x + x2 = 2 + -2 + 7x + -7x Combine like terms: 2 + -2 = 0 36 + -27x + x2 = 0 + 7x + -7x 36 + -27x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 36 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -27x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -27x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -27x + x2 = 0 + -36 -27x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -27x + x2 = -36 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -36 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -36 + 182.25 Combine like terms: -36 + 182.25 = 146.25 182.25 + -27x + x2 = 146.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + -13.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + -13.5 = 12.093386622 Simplifying x + -13.5 = 12.093386622 Reorder the terms: -13.5 + x = 12.093386622 Solving -13.5 + x = 12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 12.093386622 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 12.093386622 + 13.5 x = 12.093386622 + 13.5 Combine like terms: 12.093386622 + 13.5 = 25.593386622 x = 25.593386622 Simplifying x = 25.593386622Subproblem 2
x + -13.5 = -12.093386622 Simplifying x + -13.5 = -12.093386622 Reorder the terms: -13.5 + x = -12.093386622 Solving -13.5 + x = -12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -12.093386622 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -12.093386622 + 13.5 x = -12.093386622 + 13.5 Combine like terms: -12.093386622 + 13.5 = 1.406613378 x = 1.406613378 Simplifying x = 1.406613378Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.593386622, 1.406613378}
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