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Simplifying 4x2 + 48x + 20 = 16x + -39 Reorder the terms: 20 + 48x + 4x2 = 16x + -39 Reorder the terms: 20 + 48x + 4x2 = -39 + 16x Solving 20 + 48x + 4x2 = -39 + 16x Solving for variable 'x'. Reorder the terms: 20 + 39 + 48x + -16x + 4x2 = -39 + 16x + 39 + -16x Combine like terms: 20 + 39 = 59 59 + 48x + -16x + 4x2 = -39 + 16x + 39 + -16x Combine like terms: 48x + -16x = 32x 59 + 32x + 4x2 = -39 + 16x + 39 + -16x Reorder the terms: 59 + 32x + 4x2 = -39 + 39 + 16x + -16x Combine like terms: -39 + 39 = 0 59 + 32x + 4x2 = 0 + 16x + -16x 59 + 32x + 4x2 = 16x + -16x Combine like terms: 16x + -16x = 0 59 + 32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 14.75 + 8x + x2 = 0 Move the constant term to the right: Add '-14.75' to each side of the equation. 14.75 + 8x + -14.75 + x2 = 0 + -14.75 Reorder the terms: 14.75 + -14.75 + 8x + x2 = 0 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + 8x + x2 = 0 + -14.75 8x + x2 = 0 + -14.75 Combine like terms: 0 + -14.75 = -14.75 8x + x2 = -14.75 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 = -14.75 + 16 Reorder the terms: 16 + 8x + x2 = -14.75 + 16 Combine like terms: -14.75 + 16 = 1.25 16 + 8x + x2 = 1.25 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 4) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 4 = 1.118033989 Simplifying x + 4 = 1.118033989 Reorder the terms: 4 + x = 1.118033989 Solving 4 + x = 1.118033989 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 = 1.118033989 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.118033989 + -4 x = 1.118033989 + -4 Combine like terms: 1.118033989 + -4 = -2.881966011 x = -2.881966011 Simplifying x = -2.881966011Subproblem 2
x + 4 = -1.118033989 Simplifying x + 4 = -1.118033989 Reorder the terms: 4 + x = -1.118033989 Solving 4 + x = -1.118033989 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 = -1.118033989 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.118033989 + -4 x = -1.118033989 + -4 Combine like terms: -1.118033989 + -4 = -5.118033989 x = -5.118033989 Simplifying x = -5.118033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.881966011, -5.118033989}
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