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Simplifying 2x2 + 4x + 4 = 1600 Reorder the terms: 4 + 4x + 2x2 = 1600 Solving 4 + 4x + 2x2 = 1600 Solving for variable 'x'. Reorder the terms: 4 + -1600 + 4x + 2x2 = 1600 + -1600 Combine like terms: 4 + -1600 = -1596 -1596 + 4x + 2x2 = 1600 + -1600 Combine like terms: 1600 + -1600 = 0 -1596 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-798 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-798 + 2x + x2)' equal to zero and attempt to solve: Simplifying -798 + 2x + x2 = 0 Solving -798 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '798' to each side of the equation. -798 + 2x + 798 + x2 = 0 + 798 Reorder the terms: -798 + 798 + 2x + x2 = 0 + 798 Combine like terms: -798 + 798 = 0 0 + 2x + x2 = 0 + 798 2x + x2 = 0 + 798 Combine like terms: 0 + 798 = 798 2x + x2 = 798 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 798 + 1 Reorder the terms: 1 + 2x + x2 = 798 + 1 Combine like terms: 798 + 1 = 799 1 + 2x + x2 = 799 Factor a perfect square on the left side: (x + 1)(x + 1) = 799 Calculate the square root of the right side: 28.26658805 Break this problem into two subproblems by setting (x + 1) equal to 28.26658805 and -28.26658805.Subproblem 1
x + 1 = 28.26658805 Simplifying x + 1 = 28.26658805 Reorder the terms: 1 + x = 28.26658805 Solving 1 + x = 28.26658805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 28.26658805 + -1 Combine like terms: 1 + -1 = 0 0 + x = 28.26658805 + -1 x = 28.26658805 + -1 Combine like terms: 28.26658805 + -1 = 27.26658805 x = 27.26658805 Simplifying x = 27.26658805Subproblem 2
x + 1 = -28.26658805 Simplifying x + 1 = -28.26658805 Reorder the terms: 1 + x = -28.26658805 Solving 1 + x = -28.26658805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -28.26658805 + -1 Combine like terms: 1 + -1 = 0 0 + x = -28.26658805 + -1 x = -28.26658805 + -1 Combine like terms: -28.26658805 + -1 = -29.26658805 x = -29.26658805 Simplifying x = -29.26658805Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.26658805, -29.26658805}Solution
x = {27.26658805, -29.26658805}
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