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Simplifying 2x2 = 1280 + 16x Solving 2x2 = 1280 + 16x Solving for variable 'x'. Reorder the terms: -1280 + -16x + 2x2 = 1280 + 16x + -1280 + -16x Reorder the terms: -1280 + -16x + 2x2 = 1280 + -1280 + 16x + -16x Combine like terms: 1280 + -1280 = 0 -1280 + -16x + 2x2 = 0 + 16x + -16x -1280 + -16x + 2x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -1280 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-640 + -8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-640 + -8x + x2)' equal to zero and attempt to solve: Simplifying -640 + -8x + x2 = 0 Solving -640 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '640' to each side of the equation. -640 + -8x + 640 + x2 = 0 + 640 Reorder the terms: -640 + 640 + -8x + x2 = 0 + 640 Combine like terms: -640 + 640 = 0 0 + -8x + x2 = 0 + 640 -8x + x2 = 0 + 640 Combine like terms: 0 + 640 = 640 -8x + x2 = 640 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 = 640 + 16 Reorder the terms: 16 + -8x + x2 = 640 + 16 Combine like terms: 640 + 16 = 656 16 + -8x + x2 = 656 Factor a perfect square on the left side: (x + -4)(x + -4) = 656 Calculate the square root of the right side: 25.61249695 Break this problem into two subproblems by setting (x + -4) equal to 25.61249695 and -25.61249695.Subproblem 1
x + -4 = 25.61249695 Simplifying x + -4 = 25.61249695 Reorder the terms: -4 + x = 25.61249695 Solving -4 + x = 25.61249695 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 = 25.61249695 + 4 Combine like terms: -4 + 4 = 0 0 + x = 25.61249695 + 4 x = 25.61249695 + 4 Combine like terms: 25.61249695 + 4 = 29.61249695 x = 29.61249695 Simplifying x = 29.61249695Subproblem 2
x + -4 = -25.61249695 Simplifying x + -4 = -25.61249695 Reorder the terms: -4 + x = -25.61249695 Solving -4 + x = -25.61249695 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 = -25.61249695 + 4 Combine like terms: -4 + 4 = 0 0 + x = -25.61249695 + 4 x = -25.61249695 + 4 Combine like terms: -25.61249695 + 4 = -21.61249695 x = -21.61249695 Simplifying x = -21.61249695Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.61249695, -21.61249695}Solution
x = {29.61249695, -21.61249695}
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