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Simplifying 2x(2x + 4) = 100 Reorder the terms: 2x(4 + 2x) = 100 (4 * 2x + 2x * 2x) = 100 (8x + 4x2) = 100 Solving 8x + 4x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 8x + 4x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + 2x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + 2x + x2)' equal to zero and attempt to solve: Simplifying -25 + 2x + x2 = 0 Solving -25 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 2x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 2x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2x + x2 = 0 + 25 2x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 2x + x2 = 25 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 = 25 + 1 Reorder the terms: 1 + 2x + x2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2x + x2 = 26 Factor a perfect square on the left side: (x + 1)(x + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 1 = 5.099019514 Simplifying x + 1 = 5.099019514 Reorder the terms: 1 + x = 5.099019514 Solving 1 + x = 5.099019514 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 = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.099019514 + -1 x = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 x = 4.099019514 Simplifying x = 4.099019514Subproblem 2
x + 1 = -5.099019514 Simplifying x + 1 = -5.099019514 Reorder the terms: 1 + x = -5.099019514 Solving 1 + x = -5.099019514 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 = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.099019514 + -1 x = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 x = -6.099019514 Simplifying x = -6.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.099019514, -6.099019514}Solution
x = {4.099019514, -6.099019514}
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