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Simplifying 0 = -9x2 + 3x + 9 Reorder the terms: 0 = 9 + 3x + -9x2 Solving 0 = 9 + 3x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -3x + 9x2 = 9 + 3x + -9x2 + -9 + -3x + 9x2 Reorder the terms: -9 + -3x + 9x2 = 9 + -9 + 3x + -3x + -9x2 + 9x2 Combine like terms: 9 + -9 = 0 -9 + -3x + 9x2 = 0 + 3x + -3x + -9x2 + 9x2 -9 + -3x + 9x2 = 3x + -3x + -9x2 + 9x2 Combine like terms: 3x + -3x = 0 -9 + -3x + 9x2 = 0 + -9x2 + 9x2 -9 + -3x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -9 + -3x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -1x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -3 + -1x + 3x2 = 0 Solving -3 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.3333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.3333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.3333333333x + x2 = 0 + 1 -0.3333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.3333333333x + x2 = 1 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 1 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 1 + 0.02777777779 Combine like terms: 1 + 0.02777777779 = 1.02777777779 0.02777777779 + -0.3333333333x + x2 = 1.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 1.02777777779 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.013793755 and -1.013793755.Subproblem 1
x + -0.1666666667 = 1.013793755 Simplifying x + -0.1666666667 = 1.013793755 Reorder the terms: -0.1666666667 + x = 1.013793755 Solving -0.1666666667 + x = 1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 1.013793755 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.013793755 + 0.1666666667 x = 1.013793755 + 0.1666666667 Combine like terms: 1.013793755 + 0.1666666667 = 1.1804604217 x = 1.1804604217 Simplifying x = 1.1804604217Subproblem 2
x + -0.1666666667 = -1.013793755 Simplifying x + -0.1666666667 = -1.013793755 Reorder the terms: -0.1666666667 + x = -1.013793755 Solving -0.1666666667 + x = -1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -1.013793755 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.013793755 + 0.1666666667 x = -1.013793755 + 0.1666666667 Combine like terms: -1.013793755 + 0.1666666667 = -0.8471270883 x = -0.8471270883 Simplifying x = -0.8471270883Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1804604217, -0.8471270883}Solution
x = {1.1804604217, -0.8471270883}
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