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Simplifying 4x2 + 16x + -64 = 49 Reorder the terms: -64 + 16x + 4x2 = 49 Solving -64 + 16x + 4x2 = 49 Solving for variable 'x'. Reorder the terms: -64 + -49 + 16x + 4x2 = 49 + -49 Combine like terms: -64 + -49 = -113 -113 + 16x + 4x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -113 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -28.25 + 4x + x2 = 0 Move the constant term to the right: Add '28.25' to each side of the equation. -28.25 + 4x + 28.25 + x2 = 0 + 28.25 Reorder the terms: -28.25 + 28.25 + 4x + x2 = 0 + 28.25 Combine like terms: -28.25 + 28.25 = 0.00 0.00 + 4x + x2 = 0 + 28.25 4x + x2 = 0 + 28.25 Combine like terms: 0 + 28.25 = 28.25 4x + x2 = 28.25 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 28.25 + 4 Reorder the terms: 4 + 4x + x2 = 28.25 + 4 Combine like terms: 28.25 + 4 = 32.25 4 + 4x + x2 = 32.25 Factor a perfect square on the left side: (x + 2)(x + 2) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + 2) equal to 5.678908346 and -5.678908346.Subproblem 1
x + 2 = 5.678908346 Simplifying x + 2 = 5.678908346 Reorder the terms: 2 + x = 5.678908346 Solving 2 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.678908346 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.678908346 + -2 x = 5.678908346 + -2 Combine like terms: 5.678908346 + -2 = 3.678908346 x = 3.678908346 Simplifying x = 3.678908346Subproblem 2
x + 2 = -5.678908346 Simplifying x + 2 = -5.678908346 Reorder the terms: 2 + x = -5.678908346 Solving 2 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.678908346 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.678908346 + -2 x = -5.678908346 + -2 Combine like terms: -5.678908346 + -2 = -7.678908346 x = -7.678908346 Simplifying x = -7.678908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.678908346, -7.678908346}
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