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Simplifying 333x2 + 16x + -192 = 0 Reorder the terms: -192 + 16x + 333x2 = 0 Solving -192 + 16x + 333x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 333 the coefficient of the squared term: Divide each side by '333'. -0.5765765766 + 0.04804804805x + x2 = 0 Move the constant term to the right: Add '0.5765765766' to each side of the equation. -0.5765765766 + 0.04804804805x + 0.5765765766 + x2 = 0 + 0.5765765766 Reorder the terms: -0.5765765766 + 0.5765765766 + 0.04804804805x + x2 = 0 + 0.5765765766 Combine like terms: -0.5765765766 + 0.5765765766 = 0.0000000000 0.0000000000 + 0.04804804805x + x2 = 0 + 0.5765765766 0.04804804805x + x2 = 0 + 0.5765765766 Combine like terms: 0 + 0.5765765766 = 0.5765765766 0.04804804805x + x2 = 0.5765765766 The x term is 0.04804804805x. Take half its coefficient (0.02402402403). Square it (0.0005771537306) and add it to both sides. Add '0.0005771537306' to each side of the equation. 0.04804804805x + 0.0005771537306 + x2 = 0.5765765766 + 0.0005771537306 Reorder the terms: 0.0005771537306 + 0.04804804805x + x2 = 0.5765765766 + 0.0005771537306 Combine like terms: 0.5765765766 + 0.0005771537306 = 0.5771537303306 0.0005771537306 + 0.04804804805x + x2 = 0.5771537303306 Factor a perfect square on the left side: (x + 0.02402402403)(x + 0.02402402403) = 0.5771537303306 Calculate the square root of the right side: 0.759706345 Break this problem into two subproblems by setting (x + 0.02402402403) equal to 0.759706345 and -0.759706345.Subproblem 1
x + 0.02402402403 = 0.759706345 Simplifying x + 0.02402402403 = 0.759706345 Reorder the terms: 0.02402402403 + x = 0.759706345 Solving 0.02402402403 + x = 0.759706345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02402402403' to each side of the equation. 0.02402402403 + -0.02402402403 + x = 0.759706345 + -0.02402402403 Combine like terms: 0.02402402403 + -0.02402402403 = 0.00000000000 0.00000000000 + x = 0.759706345 + -0.02402402403 x = 0.759706345 + -0.02402402403 Combine like terms: 0.759706345 + -0.02402402403 = 0.73568232097 x = 0.73568232097 Simplifying x = 0.73568232097Subproblem 2
x + 0.02402402403 = -0.759706345 Simplifying x + 0.02402402403 = -0.759706345 Reorder the terms: 0.02402402403 + x = -0.759706345 Solving 0.02402402403 + x = -0.759706345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02402402403' to each side of the equation. 0.02402402403 + -0.02402402403 + x = -0.759706345 + -0.02402402403 Combine like terms: 0.02402402403 + -0.02402402403 = 0.00000000000 0.00000000000 + x = -0.759706345 + -0.02402402403 x = -0.759706345 + -0.02402402403 Combine like terms: -0.759706345 + -0.02402402403 = -0.78373036903 x = -0.78373036903 Simplifying x = -0.78373036903Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.73568232097, -0.78373036903}
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