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Simplifying 12(23x + -12) = x2 Reorder the terms: 12(-12 + 23x) = x2 (-12 * 12 + 23x * 12) = x2 (-144 + 276x) = x2 Solving -144 + 276x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -144 + 276x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 144 + -276x + x2 = 0 Move the constant term to the right: Add '-144' to each side of the equation. 144 + -276x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + -276x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -276x + x2 = 0 + -144 -276x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 -276x + x2 = -144 The x term is -276x. Take half its coefficient (-138). Square it (19044) and add it to both sides. Add '19044' to each side of the equation. -276x + 19044 + x2 = -144 + 19044 Reorder the terms: 19044 + -276x + x2 = -144 + 19044 Combine like terms: -144 + 19044 = 18900 19044 + -276x + x2 = 18900 Factor a perfect square on the left side: (x + -138)(x + -138) = 18900 Calculate the square root of the right side: 137.477270849 Break this problem into two subproblems by setting (x + -138) equal to 137.477270849 and -137.477270849.Subproblem 1
x + -138 = 137.477270849 Simplifying x + -138 = 137.477270849 Reorder the terms: -138 + x = 137.477270849 Solving -138 + x = 137.477270849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '138' to each side of the equation. -138 + 138 + x = 137.477270849 + 138 Combine like terms: -138 + 138 = 0 0 + x = 137.477270849 + 138 x = 137.477270849 + 138 Combine like terms: 137.477270849 + 138 = 275.477270849 x = 275.477270849 Simplifying x = 275.477270849Subproblem 2
x + -138 = -137.477270849 Simplifying x + -138 = -137.477270849 Reorder the terms: -138 + x = -137.477270849 Solving -138 + x = -137.477270849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '138' to each side of the equation. -138 + 138 + x = -137.477270849 + 138 Combine like terms: -138 + 138 = 0 0 + x = -137.477270849 + 138 x = -137.477270849 + 138 Combine like terms: -137.477270849 + 138 = 0.522729151 x = 0.522729151 Simplifying x = 0.522729151Solution
The solution to the problem is based on the solutions from the subproblems. x = {275.477270849, 0.522729151}
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