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Simplifying 17.2515 + 16.43x + -165x2 = 0 Solving 17.2515 + 16.43x + -165x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -165 the coefficient of the squared term: Divide each side by '-165'. -0.1045545455 + -0.09957575758x + x2 = 0 Move the constant term to the right: Add '0.1045545455' to each side of the equation. -0.1045545455 + -0.09957575758x + 0.1045545455 + x2 = 0 + 0.1045545455 Reorder the terms: -0.1045545455 + 0.1045545455 + -0.09957575758x + x2 = 0 + 0.1045545455 Combine like terms: -0.1045545455 + 0.1045545455 = 0.0000000000 0.0000000000 + -0.09957575758x + x2 = 0 + 0.1045545455 -0.09957575758x + x2 = 0 + 0.1045545455 Combine like terms: 0 + 0.1045545455 = 0.1045545455 -0.09957575758x + x2 = 0.1045545455 The x term is -0.09957575758x. Take half its coefficient (-0.04978787879). Square it (0.002478832874) and add it to both sides. Add '0.002478832874' to each side of the equation. -0.09957575758x + 0.002478832874 + x2 = 0.1045545455 + 0.002478832874 Reorder the terms: 0.002478832874 + -0.09957575758x + x2 = 0.1045545455 + 0.002478832874 Combine like terms: 0.1045545455 + 0.002478832874 = 0.107033378374 0.002478832874 + -0.09957575758x + x2 = 0.107033378374 Factor a perfect square on the left side: (x + -0.04978787879)(x + -0.04978787879) = 0.107033378374 Calculate the square root of the right side: 0.327159561 Break this problem into two subproblems by setting (x + -0.04978787879) equal to 0.327159561 and -0.327159561.Subproblem 1
x + -0.04978787879 = 0.327159561 Simplifying x + -0.04978787879 = 0.327159561 Reorder the terms: -0.04978787879 + x = 0.327159561 Solving -0.04978787879 + x = 0.327159561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04978787879' to each side of the equation. -0.04978787879 + 0.04978787879 + x = 0.327159561 + 0.04978787879 Combine like terms: -0.04978787879 + 0.04978787879 = 0.00000000000 0.00000000000 + x = 0.327159561 + 0.04978787879 x = 0.327159561 + 0.04978787879 Combine like terms: 0.327159561 + 0.04978787879 = 0.37694743979 x = 0.37694743979 Simplifying x = 0.37694743979Subproblem 2
x + -0.04978787879 = -0.327159561 Simplifying x + -0.04978787879 = -0.327159561 Reorder the terms: -0.04978787879 + x = -0.327159561 Solving -0.04978787879 + x = -0.327159561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04978787879' to each side of the equation. -0.04978787879 + 0.04978787879 + x = -0.327159561 + 0.04978787879 Combine like terms: -0.04978787879 + 0.04978787879 = 0.00000000000 0.00000000000 + x = -0.327159561 + 0.04978787879 x = -0.327159561 + 0.04978787879 Combine like terms: -0.327159561 + 0.04978787879 = -0.27737168221 x = -0.27737168221 Simplifying x = -0.27737168221Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.37694743979, -0.27737168221}
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