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Simplifying 0 = 3x2 + -63x + 170 Reorder the terms: 0 = 170 + -63x + 3x2 Solving 0 = 170 + -63x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -170 = -170 -170 + 63x + -3x2 = 170 + -63x + 3x2 + -170 + 63x + -3x2 Reorder the terms: -170 + 63x + -3x2 = 170 + -170 + -63x + 63x + 3x2 + -3x2 Combine like terms: 170 + -170 = 0 -170 + 63x + -3x2 = 0 + -63x + 63x + 3x2 + -3x2 -170 + 63x + -3x2 = -63x + 63x + 3x2 + -3x2 Combine like terms: -63x + 63x = 0 -170 + 63x + -3x2 = 0 + 3x2 + -3x2 -170 + 63x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -170 + 63x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 56.66666667 + -21x + x2 = 0 Move the constant term to the right: Add '-56.66666667' to each side of the equation. 56.66666667 + -21x + -56.66666667 + x2 = 0 + -56.66666667 Reorder the terms: 56.66666667 + -56.66666667 + -21x + x2 = 0 + -56.66666667 Combine like terms: 56.66666667 + -56.66666667 = 0.00000000 0.00000000 + -21x + x2 = 0 + -56.66666667 -21x + x2 = 0 + -56.66666667 Combine like terms: 0 + -56.66666667 = -56.66666667 -21x + x2 = -56.66666667 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -56.66666667 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -56.66666667 + 110.25 Combine like terms: -56.66666667 + 110.25 = 53.58333333 110.25 + -21x + x2 = 53.58333333 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 53.58333333 Calculate the square root of the right side: 7.320063752 Break this problem into two subproblems by setting (x + -10.5) equal to 7.320063752 and -7.320063752.Subproblem 1
x + -10.5 = 7.320063752 Simplifying x + -10.5 = 7.320063752 Reorder the terms: -10.5 + x = 7.320063752 Solving -10.5 + x = 7.320063752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 7.320063752 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 7.320063752 + 10.5 x = 7.320063752 + 10.5 Combine like terms: 7.320063752 + 10.5 = 17.820063752 x = 17.820063752 Simplifying x = 17.820063752Subproblem 2
x + -10.5 = -7.320063752 Simplifying x + -10.5 = -7.320063752 Reorder the terms: -10.5 + x = -7.320063752 Solving -10.5 + x = -7.320063752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -7.320063752 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -7.320063752 + 10.5 x = -7.320063752 + 10.5 Combine like terms: -7.320063752 + 10.5 = 3.179936248 x = 3.179936248 Simplifying x = 3.179936248Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.820063752, 3.179936248}
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