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Simplifying 4x(90 + -1x) + 6 = 180 + -1x (90 * 4x + -1x * 4x) + 6 = 180 + -1x (360x + -4x2) + 6 = 180 + -1x Reorder the terms: 6 + 360x + -4x2 = 180 + -1x Solving 6 + 360x + -4x2 = 180 + -1x Solving for variable 'x'. Reorder the terms: 6 + -180 + 360x + x + -4x2 = 180 + -1x + -180 + x Combine like terms: 6 + -180 = -174 -174 + 360x + x + -4x2 = 180 + -1x + -180 + x Combine like terms: 360x + x = 361x -174 + 361x + -4x2 = 180 + -1x + -180 + x Reorder the terms: -174 + 361x + -4x2 = 180 + -180 + -1x + x Combine like terms: 180 + -180 = 0 -174 + 361x + -4x2 = 0 + -1x + x -174 + 361x + -4x2 = -1x + x Combine like terms: -1x + x = 0 -174 + 361x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 43.5 + -90.25x + x2 = 0 Move the constant term to the right: Add '-43.5' to each side of the equation. 43.5 + -90.25x + -43.5 + x2 = 0 + -43.5 Reorder the terms: 43.5 + -43.5 + -90.25x + x2 = 0 + -43.5 Combine like terms: 43.5 + -43.5 = 0.0 0.0 + -90.25x + x2 = 0 + -43.5 -90.25x + x2 = 0 + -43.5 Combine like terms: 0 + -43.5 = -43.5 -90.25x + x2 = -43.5 The x term is -90.25x. Take half its coefficient (-45.125). Square it (2036.265625) and add it to both sides. Add '2036.265625' to each side of the equation. -90.25x + 2036.265625 + x2 = -43.5 + 2036.265625 Reorder the terms: 2036.265625 + -90.25x + x2 = -43.5 + 2036.265625 Combine like terms: -43.5 + 2036.265625 = 1992.765625 2036.265625 + -90.25x + x2 = 1992.765625 Factor a perfect square on the left side: (x + -45.125)(x + -45.125) = 1992.765625 Calculate the square root of the right side: 44.640403504 Break this problem into two subproblems by setting (x + -45.125) equal to 44.640403504 and -44.640403504.Subproblem 1
x + -45.125 = 44.640403504 Simplifying x + -45.125 = 44.640403504 Reorder the terms: -45.125 + x = 44.640403504 Solving -45.125 + x = 44.640403504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.125' to each side of the equation. -45.125 + 45.125 + x = 44.640403504 + 45.125 Combine like terms: -45.125 + 45.125 = 0.000 0.000 + x = 44.640403504 + 45.125 x = 44.640403504 + 45.125 Combine like terms: 44.640403504 + 45.125 = 89.765403504 x = 89.765403504 Simplifying x = 89.765403504Subproblem 2
x + -45.125 = -44.640403504 Simplifying x + -45.125 = -44.640403504 Reorder the terms: -45.125 + x = -44.640403504 Solving -45.125 + x = -44.640403504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.125' to each side of the equation. -45.125 + 45.125 + x = -44.640403504 + 45.125 Combine like terms: -45.125 + 45.125 = 0.000 0.000 + x = -44.640403504 + 45.125 x = -44.640403504 + 45.125 Combine like terms: -44.640403504 + 45.125 = 0.484596496 x = 0.484596496 Simplifying x = 0.484596496Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.765403504, 0.484596496}
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