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Simplifying 21x2 + -27x + -3 = 0 Reorder the terms: -3 + -27x + 21x2 = 0 Solving -3 + -27x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -9x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -9x + 7x2)' equal to zero and attempt to solve: Simplifying -1 + -9x + 7x2 = 0 Solving -1 + -9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -1.285714286x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -1.285714286x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -1.285714286x + x2 = 0 + 0.1428571429 -1.285714286x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -1.285714286x + x2 = 0.1428571429 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = 0.1428571429 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 0.1428571429 + 0.4132653063 Combine like terms: 0.1428571429 + 0.4132653063 = 0.5561224492 0.4132653063 + -1.285714286x + x2 = 0.5561224492 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 0.5561224492 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (x + -0.642857143) equal to 0.745736179 and -0.745736179.Subproblem 1
x + -0.642857143 = 0.745736179 Simplifying x + -0.642857143 = 0.745736179 Reorder the terms: -0.642857143 + x = 0.745736179 Solving -0.642857143 + x = 0.745736179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = 0.745736179 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 0.745736179 + 0.642857143 x = 0.745736179 + 0.642857143 Combine like terms: 0.745736179 + 0.642857143 = 1.388593322 x = 1.388593322 Simplifying x = 1.388593322Subproblem 2
x + -0.642857143 = -0.745736179 Simplifying x + -0.642857143 = -0.745736179 Reorder the terms: -0.642857143 + x = -0.745736179 Solving -0.642857143 + x = -0.745736179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = -0.745736179 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -0.745736179 + 0.642857143 x = -0.745736179 + 0.642857143 Combine like terms: -0.745736179 + 0.642857143 = -0.102879036 x = -0.102879036 Simplifying x = -0.102879036Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.388593322, -0.102879036}Solution
x = {1.388593322, -0.102879036}
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