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Simplifying 80000000000 = 2x2 + -16x + 104 Reorder the terms: 80000000000 = 104 + -16x + 2x2 Solving 80000000000 = 104 + -16x + 2x2 Solving for variable 'x'. Combine like terms: 80000000000 + -104 = 79999999896 79999999896 + 16x + -2x2 = 104 + -16x + 2x2 + -104 + 16x + -2x2 Reorder the terms: 79999999896 + 16x + -2x2 = 104 + -104 + -16x + 16x + 2x2 + -2x2 Combine like terms: 104 + -104 = 0 79999999896 + 16x + -2x2 = 0 + -16x + 16x + 2x2 + -2x2 79999999896 + 16x + -2x2 = -16x + 16x + 2x2 + -2x2 Combine like terms: -16x + 16x = 0 79999999896 + 16x + -2x2 = 0 + 2x2 + -2x2 79999999896 + 16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 79999999896 + 16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(39999999950 + 8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(39999999950 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying 39999999950 + 8x + -1x2 = 0 Solving 39999999950 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39999999950 + -8x + x2 = 0 Move the constant term to the right: Add '39999999950' to each side of the equation. -39999999950 + -8x + 39999999950 + x2 = 0 + 39999999950 Reorder the terms: -39999999950 + 39999999950 + -8x + x2 = 0 + 39999999950 Combine like terms: -39999999950 + 39999999950 = 0 0 + -8x + x2 = 0 + 39999999950 -8x + x2 = 0 + 39999999950 Combine like terms: 0 + 39999999950 = 39999999950 -8x + x2 = 39999999950 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 = 39999999950 + 16 Reorder the terms: 16 + -8x + x2 = 39999999950 + 16 Combine like terms: 39999999950 + 16 = 39999999966 16 + -8x + x2 = 39999999966 Factor a perfect square on the left side: (x + -4)(x + -4) = 39999999966 Calculate the square root of the right side: 199999.999915 Break this problem into two subproblems by setting (x + -4) equal to 199999.999915 and -199999.999915.Subproblem 1
x + -4 = 199999.999915 Simplifying x + -4 = 199999.999915 Reorder the terms: -4 + x = 199999.999915 Solving -4 + x = 199999.999915 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 = 199999.999915 + 4 Combine like terms: -4 + 4 = 0 0 + x = 199999.999915 + 4 x = 199999.999915 + 4 Combine like terms: 199999.999915 + 4 = 200003.999915 x = 200003.999915 Simplifying x = 200003.999915Subproblem 2
x + -4 = -199999.999915 Simplifying x + -4 = -199999.999915 Reorder the terms: -4 + x = -199999.999915 Solving -4 + x = -199999.999915 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 = -199999.999915 + 4 Combine like terms: -4 + 4 = 0 0 + x = -199999.999915 + 4 x = -199999.999915 + 4 Combine like terms: -199999.999915 + 4 = -199995.999915 x = -199995.999915 Simplifying x = -199995.999915Solution
The solution to the problem is based on the solutions from the subproblems. x = {200003.999915, -199995.999915}Solution
x = {200003.999915, -199995.999915}
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