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Simplifying 4x2 + 16x + 64 = 65 Reorder the terms: 64 + 16x + 4x2 = 65 Solving 64 + 16x + 4x2 = 65 Solving for variable 'x'. Reorder the terms: 64 + -65 + 16x + 4x2 = 65 + -65 Combine like terms: 64 + -65 = -1 -1 + 16x + 4x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -1 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 4x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 4x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 4x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 4x + x2 = 0 + 0.25 4x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 4x + x2 = 0.25 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 = 0.25 + 4 Reorder the terms: 4 + 4x + x2 = 0.25 + 4 Combine like terms: 0.25 + 4 = 4.25 4 + 4x + x2 = 4.25 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 2) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 2 = 2.061552813 Simplifying x + 2 = 2.061552813 Reorder the terms: 2 + x = 2.061552813 Solving 2 + x = 2.061552813 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 = 2.061552813 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.061552813 + -2 x = 2.061552813 + -2 Combine like terms: 2.061552813 + -2 = 0.061552813 x = 0.061552813 Simplifying x = 0.061552813Subproblem 2
x + 2 = -2.061552813 Simplifying x + 2 = -2.061552813 Reorder the terms: 2 + x = -2.061552813 Solving 2 + x = -2.061552813 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 = -2.061552813 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.061552813 + -2 x = -2.061552813 + -2 Combine like terms: -2.061552813 + -2 = -4.061552813 x = -4.061552813 Simplifying x = -4.061552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.061552813, -4.061552813}
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