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Simplifying 24x2 + -202x + 306 = 0 Reorder the terms: 306 + -202x + 24x2 = 0 Solving 306 + -202x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(153 + -101x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(153 + -101x + 12x2)' equal to zero and attempt to solve: Simplifying 153 + -101x + 12x2 = 0 Solving 153 + -101x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 12.75 + -8.416666667x + x2 = 0 Move the constant term to the right: Add '-12.75' to each side of the equation. 12.75 + -8.416666667x + -12.75 + x2 = 0 + -12.75 Reorder the terms: 12.75 + -12.75 + -8.416666667x + x2 = 0 + -12.75 Combine like terms: 12.75 + -12.75 = 0.00 0.00 + -8.416666667x + x2 = 0 + -12.75 -8.416666667x + x2 = 0 + -12.75 Combine like terms: 0 + -12.75 = -12.75 -8.416666667x + x2 = -12.75 The x term is -8.416666667x. Take half its coefficient (-4.208333334). Square it (17.71006945) and add it to both sides. Add '17.71006945' to each side of the equation. -8.416666667x + 17.71006945 + x2 = -12.75 + 17.71006945 Reorder the terms: 17.71006945 + -8.416666667x + x2 = -12.75 + 17.71006945 Combine like terms: -12.75 + 17.71006945 = 4.96006945 17.71006945 + -8.416666667x + x2 = 4.96006945 Factor a perfect square on the left side: (x + -4.208333334)(x + -4.208333334) = 4.96006945 Calculate the square root of the right side: 2.227121337 Break this problem into two subproblems by setting (x + -4.208333334) equal to 2.227121337 and -2.227121337.Subproblem 1
x + -4.208333334 = 2.227121337 Simplifying x + -4.208333334 = 2.227121337 Reorder the terms: -4.208333334 + x = 2.227121337 Solving -4.208333334 + x = 2.227121337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.208333334' to each side of the equation. -4.208333334 + 4.208333334 + x = 2.227121337 + 4.208333334 Combine like terms: -4.208333334 + 4.208333334 = 0.000000000 0.000000000 + x = 2.227121337 + 4.208333334 x = 2.227121337 + 4.208333334 Combine like terms: 2.227121337 + 4.208333334 = 6.435454671 x = 6.435454671 Simplifying x = 6.435454671Subproblem 2
x + -4.208333334 = -2.227121337 Simplifying x + -4.208333334 = -2.227121337 Reorder the terms: -4.208333334 + x = -2.227121337 Solving -4.208333334 + x = -2.227121337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.208333334' to each side of the equation. -4.208333334 + 4.208333334 + x = -2.227121337 + 4.208333334 Combine like terms: -4.208333334 + 4.208333334 = 0.000000000 0.000000000 + x = -2.227121337 + 4.208333334 x = -2.227121337 + 4.208333334 Combine like terms: -2.227121337 + 4.208333334 = 1.981211997 x = 1.981211997 Simplifying x = 1.981211997Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.435454671, 1.981211997}Solution
x = {6.435454671, 1.981211997}
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