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Simplifying 2x2 + 16x + -28 = 0 Reorder the terms: -28 + 16x + 2x2 = 0 Solving -28 + 16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + 8x + x2)' equal to zero and attempt to solve: Simplifying -14 + 8x + x2 = 0 Solving -14 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 8x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 8x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 8x + x2 = 0 + 14 8x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 8x + x2 = 14 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 = 14 + 16 Reorder the terms: 16 + 8x + x2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + 8x + x2 = 30 Factor a perfect square on the left side: (x + 4)(x + 4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 4) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 4 = 5.477225575 Simplifying x + 4 = 5.477225575 Reorder the terms: 4 + x = 5.477225575 Solving 4 + x = 5.477225575 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 = 5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.477225575 + -4 x = 5.477225575 + -4 Combine like terms: 5.477225575 + -4 = 1.477225575 x = 1.477225575 Simplifying x = 1.477225575Subproblem 2
x + 4 = -5.477225575 Simplifying x + 4 = -5.477225575 Reorder the terms: 4 + x = -5.477225575 Solving 4 + x = -5.477225575 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 = -5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.477225575 + -4 x = -5.477225575 + -4 Combine like terms: -5.477225575 + -4 = -9.477225575 x = -9.477225575 Simplifying x = -9.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.477225575, -9.477225575}Solution
x = {1.477225575, -9.477225575}
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