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Simplifying 63x2 + -9x + -24 = 0 Reorder the terms: -24 + -9x + 63x2 = 0 Solving -24 + -9x + 63x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -3x + 21x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -3x + 21x2)' equal to zero and attempt to solve: Simplifying -8 + -3x + 21x2 = 0 Solving -8 + -3x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.380952381 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.380952381' to each side of the equation. -0.380952381 + -0.1428571429x + 0.380952381 + x2 = 0 + 0.380952381 Reorder the terms: -0.380952381 + 0.380952381 + -0.1428571429x + x2 = 0 + 0.380952381 Combine like terms: -0.380952381 + 0.380952381 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 0.380952381 -0.1428571429x + x2 = 0 + 0.380952381 Combine like terms: 0 + 0.380952381 = 0.380952381 -0.1428571429x + x2 = 0.380952381 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 0.380952381 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.380952381 + 0.005102040819 Combine like terms: 0.380952381 + 0.005102040819 = 0.386054421819 0.005102040819 + -0.1428571429x + x2 = 0.386054421819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.386054421819 Calculate the square root of the right side: 0.621332779 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.621332779 and -0.621332779.Subproblem 1
x + -0.07142857145 = 0.621332779 Simplifying x + -0.07142857145 = 0.621332779 Reorder the terms: -0.07142857145 + x = 0.621332779 Solving -0.07142857145 + x = 0.621332779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.621332779 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.621332779 + 0.07142857145 x = 0.621332779 + 0.07142857145 Combine like terms: 0.621332779 + 0.07142857145 = 0.69276135045 x = 0.69276135045 Simplifying x = 0.69276135045Subproblem 2
x + -0.07142857145 = -0.621332779 Simplifying x + -0.07142857145 = -0.621332779 Reorder the terms: -0.07142857145 + x = -0.621332779 Solving -0.07142857145 + x = -0.621332779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.621332779 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.621332779 + 0.07142857145 x = -0.621332779 + 0.07142857145 Combine like terms: -0.621332779 + 0.07142857145 = -0.54990420755 x = -0.54990420755 Simplifying x = -0.54990420755Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.69276135045, -0.54990420755}Solution
x = {0.69276135045, -0.54990420755}
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