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Simplifying 99x2 + -2x + -16 = 0 Reorder the terms: -16 + -2x + 99x2 = 0 Solving -16 + -2x + 99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 99 the coefficient of the squared term: Divide each side by '99'. -0.1616161616 + -0.0202020202x + x2 = 0 Move the constant term to the right: Add '0.1616161616' to each side of the equation. -0.1616161616 + -0.0202020202x + 0.1616161616 + x2 = 0 + 0.1616161616 Reorder the terms: -0.1616161616 + 0.1616161616 + -0.0202020202x + x2 = 0 + 0.1616161616 Combine like terms: -0.1616161616 + 0.1616161616 = 0.0000000000 0.0000000000 + -0.0202020202x + x2 = 0 + 0.1616161616 -0.0202020202x + x2 = 0 + 0.1616161616 Combine like terms: 0 + 0.1616161616 = 0.1616161616 -0.0202020202x + x2 = 0.1616161616 The x term is -0.0202020202x. Take half its coefficient (-0.0101010101). Square it (0.0001020304050) and add it to both sides. Add '0.0001020304050' to each side of the equation. -0.0202020202x + 0.0001020304050 + x2 = 0.1616161616 + 0.0001020304050 Reorder the terms: 0.0001020304050 + -0.0202020202x + x2 = 0.1616161616 + 0.0001020304050 Combine like terms: 0.1616161616 + 0.0001020304050 = 0.161718192005 0.0001020304050 + -0.0202020202x + x2 = 0.161718192005 Factor a perfect square on the left side: (x + -0.0101010101)(x + -0.0101010101) = 0.161718192005 Calculate the square root of the right side: 0.402142005 Break this problem into two subproblems by setting (x + -0.0101010101) equal to 0.402142005 and -0.402142005.Subproblem 1
x + -0.0101010101 = 0.402142005 Simplifying x + -0.0101010101 = 0.402142005 Reorder the terms: -0.0101010101 + x = 0.402142005 Solving -0.0101010101 + x = 0.402142005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0101010101' to each side of the equation. -0.0101010101 + 0.0101010101 + x = 0.402142005 + 0.0101010101 Combine like terms: -0.0101010101 + 0.0101010101 = 0.0000000000 0.0000000000 + x = 0.402142005 + 0.0101010101 x = 0.402142005 + 0.0101010101 Combine like terms: 0.402142005 + 0.0101010101 = 0.4122430151 x = 0.4122430151 Simplifying x = 0.4122430151Subproblem 2
x + -0.0101010101 = -0.402142005 Simplifying x + -0.0101010101 = -0.402142005 Reorder the terms: -0.0101010101 + x = -0.402142005 Solving -0.0101010101 + x = -0.402142005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0101010101' to each side of the equation. -0.0101010101 + 0.0101010101 + x = -0.402142005 + 0.0101010101 Combine like terms: -0.0101010101 + 0.0101010101 = 0.0000000000 0.0000000000 + x = -0.402142005 + 0.0101010101 x = -0.402142005 + 0.0101010101 Combine like terms: -0.402142005 + 0.0101010101 = -0.3920409949 x = -0.3920409949 Simplifying x = -0.3920409949Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4122430151, -0.3920409949}
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