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Simplifying 48 + x(x + -44) = 180 Reorder the terms: 48 + x(-44 + x) = 180 48 + (-44 * x + x * x) = 180 48 + (-44x + x2) = 180 Solving 48 + -44x + x2 = 180 Solving for variable 'x'. Reorder the terms: 48 + -180 + -44x + x2 = 180 + -180 Combine like terms: 48 + -180 = -132 -132 + -44x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -132 + -44x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + -44x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + -44x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + -44x + x2 = 0 + 132 -44x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 -44x + x2 = 132 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = 132 + 484 Reorder the terms: 484 + -44x + x2 = 132 + 484 Combine like terms: 132 + 484 = 616 484 + -44x + x2 = 616 Factor a perfect square on the left side: (x + -22)(x + -22) = 616 Calculate the square root of the right side: 24.819347292 Break this problem into two subproblems by setting (x + -22) equal to 24.819347292 and -24.819347292.Subproblem 1
x + -22 = 24.819347292 Simplifying x + -22 = 24.819347292 Reorder the terms: -22 + x = 24.819347292 Solving -22 + x = 24.819347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 24.819347292 + 22 Combine like terms: -22 + 22 = 0 0 + x = 24.819347292 + 22 x = 24.819347292 + 22 Combine like terms: 24.819347292 + 22 = 46.819347292 x = 46.819347292 Simplifying x = 46.819347292Subproblem 2
x + -22 = -24.819347292 Simplifying x + -22 = -24.819347292 Reorder the terms: -22 + x = -24.819347292 Solving -22 + x = -24.819347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -24.819347292 + 22 Combine like terms: -22 + 22 = 0 0 + x = -24.819347292 + 22 x = -24.819347292 + 22 Combine like terms: -24.819347292 + 22 = -2.819347292 x = -2.819347292 Simplifying x = -2.819347292Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.819347292, -2.819347292}
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