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Simplifying -23653.66987x2 + 20.41309257x + 794.6951483 = 0 Reorder the terms: 794.6951483 + 20.41309257x + -23653.66987x2 = 0 Solving 794.6951483 + 20.41309257x + -23653.66987x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -23653.66987 the coefficient of the squared term: Divide each side by '-23653.66987'. -0.03359711845 + -0.000862998963x + x2 = 0 Move the constant term to the right: Add '0.03359711845' to each side of the equation. -0.03359711845 + -0.000862998963x + 0.03359711845 + x2 = 0 + 0.03359711845 Reorder the terms: -0.03359711845 + 0.03359711845 + -0.000862998963x + x2 = 0 + 0.03359711845 Combine like terms: -0.03359711845 + 0.03359711845 = 0.00000000000 0.00000000000 + -0.000862998963x + x2 = 0 + 0.03359711845 -0.000862998963x + x2 = 0 + 0.03359711845 Combine like terms: 0 + 0.03359711845 = 0.03359711845 -0.000862998963x + x2 = 0.03359711845 The x term is -0.000862998963x. Take half its coefficient (-0.0004314994815). Square it (0.0000001861918025) and add it to both sides. Add '0.0000001861918025' to each side of the equation. -0.000862998963x + 0.0000001861918025 + x2 = 0.03359711845 + 0.0000001861918025 Reorder the terms: 0.0000001861918025 + -0.000862998963x + x2 = 0.03359711845 + 0.0000001861918025 Combine like terms: 0.03359711845 + 0.0000001861918025 = 0.0335973046418025 0.0000001861918025 + -0.000862998963x + x2 = 0.0335973046418025 Factor a perfect square on the left side: (x + -0.0004314994815)(x + -0.0004314994815) = 0.0335973046418025 Calculate the square root of the right side: 0.183295675 Break this problem into two subproblems by setting (x + -0.0004314994815) equal to 0.183295675 and -0.183295675.Subproblem 1
x + -0.0004314994815 = 0.183295675 Simplifying x + -0.0004314994815 = 0.183295675 Reorder the terms: -0.0004314994815 + x = 0.183295675 Solving -0.0004314994815 + x = 0.183295675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0004314994815' to each side of the equation. -0.0004314994815 + 0.0004314994815 + x = 0.183295675 + 0.0004314994815 Combine like terms: -0.0004314994815 + 0.0004314994815 = 0.0000000000000 0.0000000000000 + x = 0.183295675 + 0.0004314994815 x = 0.183295675 + 0.0004314994815 Combine like terms: 0.183295675 + 0.0004314994815 = 0.1837271744815 x = 0.1837271744815 Simplifying x = 0.1837271744815Subproblem 2
x + -0.0004314994815 = -0.183295675 Simplifying x + -0.0004314994815 = -0.183295675 Reorder the terms: -0.0004314994815 + x = -0.183295675 Solving -0.0004314994815 + x = -0.183295675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0004314994815' to each side of the equation. -0.0004314994815 + 0.0004314994815 + x = -0.183295675 + 0.0004314994815 Combine like terms: -0.0004314994815 + 0.0004314994815 = 0.0000000000000 0.0000000000000 + x = -0.183295675 + 0.0004314994815 x = -0.183295675 + 0.0004314994815 Combine like terms: -0.183295675 + 0.0004314994815 = -0.1828641755185 x = -0.1828641755185 Simplifying x = -0.1828641755185Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1837271744815, -0.1828641755185}
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