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Simplifying 38.616x2 + -1(38.616 * 0.101 + 1) * x + 38.616 * 0.0001 = 0 Multiply 38.616 * 0.101 38.616x2 + -1(3.900216 + 1) * x + 38.616 * 0.0001 = 0 Combine like terms: 3.900216 + 1 = 4.900216 38.616x2 + -1(4.900216) * x + 38.616 * 0.0001 = 0 Multiply -1 * 4.900216 38.616x2 + -4.900216x + 38.616 * 0.0001 = 0 Multiply 38.616 * 0.0001 38.616x2 + -4.900216x + 0.0038616 = 0 Reorder the terms: 0.0038616 + -4.900216x + 38.616x2 = 0 Solving 0.0038616 + -4.900216x + 38.616x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 38.616 the coefficient of the squared term: Divide each side by '38.616'. 0.0001 + -0.1268960017x + x2 = 0 Move the constant term to the right: Add '-0.0001' to each side of the equation. 0.0001 + -0.1268960017x + -0.0001 + x2 = 0 + -0.0001 Reorder the terms: 0.0001 + -0.0001 + -0.1268960017x + x2 = 0 + -0.0001 Combine like terms: 0.0001 + -0.0001 = 0.0000 0.0000 + -0.1268960017x + x2 = 0 + -0.0001 -0.1268960017x + x2 = 0 + -0.0001 Combine like terms: 0 + -0.0001 = -0.0001 -0.1268960017x + x2 = -0.0001 The x term is -0.1268960017x. Take half its coefficient (-0.06344800085). Square it (0.004025648812) and add it to both sides. Add '0.004025648812' to each side of the equation. -0.1268960017x + 0.004025648812 + x2 = -0.0001 + 0.004025648812 Reorder the terms: 0.004025648812 + -0.1268960017x + x2 = -0.0001 + 0.004025648812 Combine like terms: -0.0001 + 0.004025648812 = 0.003925648812 0.004025648812 + -0.1268960017x + x2 = 0.003925648812 Factor a perfect square on the left side: (x + -0.06344800085)(x + -0.06344800085) = 0.003925648812 Calculate the square root of the right side: 0.062654998 Break this problem into two subproblems by setting (x + -0.06344800085) equal to 0.062654998 and -0.062654998.Subproblem 1
x + -0.06344800085 = 0.062654998 Simplifying x + -0.06344800085 = 0.062654998 Reorder the terms: -0.06344800085 + x = 0.062654998 Solving -0.06344800085 + x = 0.062654998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06344800085' to each side of the equation. -0.06344800085 + 0.06344800085 + x = 0.062654998 + 0.06344800085 Combine like terms: -0.06344800085 + 0.06344800085 = 0.00000000000 0.00000000000 + x = 0.062654998 + 0.06344800085 x = 0.062654998 + 0.06344800085 Combine like terms: 0.062654998 + 0.06344800085 = 0.12610299885 x = 0.12610299885 Simplifying x = 0.12610299885Subproblem 2
x + -0.06344800085 = -0.062654998 Simplifying x + -0.06344800085 = -0.062654998 Reorder the terms: -0.06344800085 + x = -0.062654998 Solving -0.06344800085 + x = -0.062654998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06344800085' to each side of the equation. -0.06344800085 + 0.06344800085 + x = -0.062654998 + 0.06344800085 Combine like terms: -0.06344800085 + 0.06344800085 = 0.00000000000 0.00000000000 + x = -0.062654998 + 0.06344800085 x = -0.062654998 + 0.06344800085 Combine like terms: -0.062654998 + 0.06344800085 = 0.00079300285 x = 0.00079300285 Simplifying x = 0.00079300285Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12610299885, 0.00079300285}
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