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Simplifying x = (20 + -2x)(40 + -2x) Multiply (20 + -2x) * (40 + -2x) x = (20(40 + -2x) + -2x * (40 + -2x)) x = ((40 * 20 + -2x * 20) + -2x * (40 + -2x)) x = ((800 + -40x) + -2x * (40 + -2x)) x = (800 + -40x + (40 * -2x + -2x * -2x)) x = (800 + -40x + (-80x + 4x2)) Combine like terms: -40x + -80x = -120x x = (800 + -120x + 4x2) Solving x = 800 + -120x + 4x2 Solving for variable 'x'. Reorder the terms: -800 + x + 120x + -4x2 = 800 + -120x + 4x2 + -800 + 120x + -4x2 Combine like terms: x + 120x = 121x -800 + 121x + -4x2 = 800 + -120x + 4x2 + -800 + 120x + -4x2 Reorder the terms: -800 + 121x + -4x2 = 800 + -800 + -120x + 120x + 4x2 + -4x2 Combine like terms: 800 + -800 = 0 -800 + 121x + -4x2 = 0 + -120x + 120x + 4x2 + -4x2 -800 + 121x + -4x2 = -120x + 120x + 4x2 + -4x2 Combine like terms: -120x + 120x = 0 -800 + 121x + -4x2 = 0 + 4x2 + -4x2 -800 + 121x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -800 + 121x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 200 + -30.25x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -30.25x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -30.25x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -30.25x + x2 = 0 + -200 -30.25x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -30.25x + x2 = -200 The x term is -30.25x. Take half its coefficient (-15.125). Square it (228.765625) and add it to both sides. Add '228.765625' to each side of the equation. -30.25x + 228.765625 + x2 = -200 + 228.765625 Reorder the terms: 228.765625 + -30.25x + x2 = -200 + 228.765625 Combine like terms: -200 + 228.765625 = 28.765625 228.765625 + -30.25x + x2 = 28.765625 Factor a perfect square on the left side: (x + -15.125)(x + -15.125) = 28.765625 Calculate the square root of the right side: 5.363359488 Break this problem into two subproblems by setting (x + -15.125) equal to 5.363359488 and -5.363359488.Subproblem 1
x + -15.125 = 5.363359488 Simplifying x + -15.125 = 5.363359488 Reorder the terms: -15.125 + x = 5.363359488 Solving -15.125 + x = 5.363359488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.125' to each side of the equation. -15.125 + 15.125 + x = 5.363359488 + 15.125 Combine like terms: -15.125 + 15.125 = 0.000 0.000 + x = 5.363359488 + 15.125 x = 5.363359488 + 15.125 Combine like terms: 5.363359488 + 15.125 = 20.488359488 x = 20.488359488 Simplifying x = 20.488359488Subproblem 2
x + -15.125 = -5.363359488 Simplifying x + -15.125 = -5.363359488 Reorder the terms: -15.125 + x = -5.363359488 Solving -15.125 + x = -5.363359488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.125' to each side of the equation. -15.125 + 15.125 + x = -5.363359488 + 15.125 Combine like terms: -15.125 + 15.125 = 0.000 0.000 + x = -5.363359488 + 15.125 x = -5.363359488 + 15.125 Combine like terms: -5.363359488 + 15.125 = 9.761640512 x = 9.761640512 Simplifying x = 9.761640512Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.488359488, 9.761640512}
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