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Simplifying 4x2 + 32x + 48 = 225 Reorder the terms: 48 + 32x + 4x2 = 225 Solving 48 + 32x + 4x2 = 225 Solving for variable 'x'. Reorder the terms: 48 + -225 + 32x + 4x2 = 225 + -225 Combine like terms: 48 + -225 = -177 -177 + 32x + 4x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -177 + 32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -44.25 + 8x + x2 = 0 Move the constant term to the right: Add '44.25' to each side of the equation. -44.25 + 8x + 44.25 + x2 = 0 + 44.25 Reorder the terms: -44.25 + 44.25 + 8x + x2 = 0 + 44.25 Combine like terms: -44.25 + 44.25 = 0.00 0.00 + 8x + x2 = 0 + 44.25 8x + x2 = 0 + 44.25 Combine like terms: 0 + 44.25 = 44.25 8x + x2 = 44.25 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 44.25 + 16 Reorder the terms: 16 + 8x + x2 = 44.25 + 16 Combine like terms: 44.25 + 16 = 60.25 16 + 8x + x2 = 60.25 Factor a perfect square on the left side: (x + 4)(x + 4) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + 4) equal to 7.762087348 and -7.762087348.Subproblem 1
x + 4 = 7.762087348 Simplifying x + 4 = 7.762087348 Reorder the terms: 4 + x = 7.762087348 Solving 4 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 7.762087348 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.762087348 + -4 x = 7.762087348 + -4 Combine like terms: 7.762087348 + -4 = 3.762087348 x = 3.762087348 Simplifying x = 3.762087348Subproblem 2
x + 4 = -7.762087348 Simplifying x + 4 = -7.762087348 Reorder the terms: 4 + x = -7.762087348 Solving 4 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -7.762087348 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.762087348 + -4 x = -7.762087348 + -4 Combine like terms: -7.762087348 + -4 = -11.762087348 x = -11.762087348 Simplifying x = -11.762087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.762087348, -11.762087348}
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