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Simplifying 2x2 + 16x = 88 Reorder the terms: 16x + 2x2 = 88 Solving 16x + 2x2 = 88 Solving for variable 'x'. Reorder the terms: -88 + 16x + 2x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-44 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-44 + 8x + x2)' equal to zero and attempt to solve: Simplifying -44 + 8x + x2 = 0 Solving -44 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 8x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 8x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 8x + x2 = 0 + 44 8x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 8x + x2 = 44 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 = 44 + 16 Reorder the terms: 16 + 8x + x2 = 44 + 16 Combine like terms: 44 + 16 = 60 16 + 8x + x2 = 60 Factor a perfect square on the left side: (x + 4)(x + 4) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 4) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 4 = 7.745966692 Simplifying x + 4 = 7.745966692 Reorder the terms: 4 + x = 7.745966692 Solving 4 + x = 7.745966692 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 = 7.745966692 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.745966692 + -4 x = 7.745966692 + -4 Combine like terms: 7.745966692 + -4 = 3.745966692 x = 3.745966692 Simplifying x = 3.745966692Subproblem 2
x + 4 = -7.745966692 Simplifying x + 4 = -7.745966692 Reorder the terms: 4 + x = -7.745966692 Solving 4 + x = -7.745966692 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 = -7.745966692 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.745966692 + -4 x = -7.745966692 + -4 Combine like terms: -7.745966692 + -4 = -11.745966692 x = -11.745966692 Simplifying x = -11.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.745966692, -11.745966692}Solution
x = {3.745966692, -11.745966692}
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