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Simplifying 12x2 + -204x + 594 = 0 Reorder the terms: 594 + -204x + 12x2 = 0 Solving 594 + -204x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(99 + -34x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(99 + -34x + 2x2)' equal to zero and attempt to solve: Simplifying 99 + -34x + 2x2 = 0 Solving 99 + -34x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 49.5 + -17x + x2 = 0 Move the constant term to the right: Add '-49.5' to each side of the equation. 49.5 + -17x + -49.5 + x2 = 0 + -49.5 Reorder the terms: 49.5 + -49.5 + -17x + x2 = 0 + -49.5 Combine like terms: 49.5 + -49.5 = 0.0 0.0 + -17x + x2 = 0 + -49.5 -17x + x2 = 0 + -49.5 Combine like terms: 0 + -49.5 = -49.5 -17x + x2 = -49.5 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -49.5 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -49.5 + 72.25 Combine like terms: -49.5 + 72.25 = 22.75 72.25 + -17x + x2 = 22.75 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + -8.5) equal to 4.769696007 and -4.769696007.Subproblem 1
x + -8.5 = 4.769696007 Simplifying x + -8.5 = 4.769696007 Reorder the terms: -8.5 + x = 4.769696007 Solving -8.5 + x = 4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 4.769696007 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 4.769696007 + 8.5 x = 4.769696007 + 8.5 Combine like terms: 4.769696007 + 8.5 = 13.269696007 x = 13.269696007 Simplifying x = 13.269696007Subproblem 2
x + -8.5 = -4.769696007 Simplifying x + -8.5 = -4.769696007 Reorder the terms: -8.5 + x = -4.769696007 Solving -8.5 + x = -4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -4.769696007 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -4.769696007 + 8.5 x = -4.769696007 + 8.5 Combine like terms: -4.769696007 + 8.5 = 3.730303993 x = 3.730303993 Simplifying x = 3.730303993Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.269696007, 3.730303993}Solution
x = {13.269696007, 3.730303993}
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