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Simplifying 10 = 0.006X2 + -0.02X Reorder the terms: 10 = -0.02X + 0.006X2 Solving 10 = -0.02X + 0.006X2 Solving for variable 'X'. Reorder the terms: 10 + 0.02X + -0.006X2 = -0.02X + 0.02X + 0.006X2 + -0.006X2 Combine like terms: -0.02X + 0.02X = 0.00 10 + 0.02X + -0.006X2 = 0.00 + 0.006X2 + -0.006X2 10 + 0.02X + -0.006X2 = 0.006X2 + -0.006X2 Combine like terms: 0.006X2 + -0.006X2 = 0.000 10 + 0.02X + -0.006X2 = 0.000 Begin completing the square. Divide all terms by -0.006 the coefficient of the squared term: Divide each side by '-0.006'. -1666.666667 + -3.333333333X + X2 = 0 Move the constant term to the right: Add '1666.666667' to each side of the equation. -1666.666667 + -3.333333333X + 1666.666667 + X2 = 0 + 1666.666667 Reorder the terms: -1666.666667 + 1666.666667 + -3.333333333X + X2 = 0 + 1666.666667 Combine like terms: -1666.666667 + 1666.666667 = 0.000000 0.000000 + -3.333333333X + X2 = 0 + 1666.666667 -3.333333333X + X2 = 0 + 1666.666667 Combine like terms: 0 + 1666.666667 = 1666.666667 -3.333333333X + X2 = 1666.666667 The X term is -3.333333333X. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333X + 2.777777779 + X2 = 1666.666667 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333X + X2 = 1666.666667 + 2.777777779 Combine like terms: 1666.666667 + 2.777777779 = 1669.444444779 2.777777779 + -3.333333333X + X2 = 1669.444444779 Factor a perfect square on the left side: (X + -1.666666667)(X + -1.666666667) = 1669.444444779 Calculate the square root of the right side: 40.858835578 Break this problem into two subproblems by setting (X + -1.666666667) equal to 40.858835578 and -40.858835578.Subproblem 1
X + -1.666666667 = 40.858835578 Simplifying X + -1.666666667 = 40.858835578 Reorder the terms: -1.666666667 + X = 40.858835578 Solving -1.666666667 + X = 40.858835578 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + X = 40.858835578 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + X = 40.858835578 + 1.666666667 X = 40.858835578 + 1.666666667 Combine like terms: 40.858835578 + 1.666666667 = 42.525502245 X = 42.525502245 Simplifying X = 42.525502245Subproblem 2
X + -1.666666667 = -40.858835578 Simplifying X + -1.666666667 = -40.858835578 Reorder the terms: -1.666666667 + X = -40.858835578 Solving -1.666666667 + X = -40.858835578 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + X = -40.858835578 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + X = -40.858835578 + 1.666666667 X = -40.858835578 + 1.666666667 Combine like terms: -40.858835578 + 1.666666667 = -39.192168911 X = -39.192168911 Simplifying X = -39.192168911Solution
The solution to the problem is based on the solutions from the subproblems. X = {42.525502245, -39.192168911}
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