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Simplifying 3x2 + 8 = 9x2 + -6x + 4 Reorder the terms: 8 + 3x2 = 9x2 + -6x + 4 Reorder the terms: 8 + 3x2 = 4 + -6x + 9x2 Solving 8 + 3x2 = 4 + -6x + 9x2 Solving for variable 'x'. Reorder the terms: 8 + -4 + 6x + 3x2 + -9x2 = 4 + -6x + 9x2 + -4 + 6x + -9x2 Combine like terms: 8 + -4 = 4 4 + 6x + 3x2 + -9x2 = 4 + -6x + 9x2 + -4 + 6x + -9x2 Combine like terms: 3x2 + -9x2 = -6x2 4 + 6x + -6x2 = 4 + -6x + 9x2 + -4 + 6x + -9x2 Reorder the terms: 4 + 6x + -6x2 = 4 + -4 + -6x + 6x + 9x2 + -9x2 Combine like terms: 4 + -4 = 0 4 + 6x + -6x2 = 0 + -6x + 6x + 9x2 + -9x2 4 + 6x + -6x2 = -6x + 6x + 9x2 + -9x2 Combine like terms: -6x + 6x = 0 4 + 6x + -6x2 = 0 + 9x2 + -9x2 4 + 6x + -6x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 4 + 6x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 3x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 3x + -3x2)' equal to zero and attempt to solve: Simplifying 2 + 3x + -3x2 = 0 Solving 2 + 3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + -1x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.6666666667 -1x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1x + x2 = 0.6666666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.6666666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.6666666667 + 0.25 Combine like terms: 0.6666666667 + 0.25 = 0.9166666667 0.25 + -1x + x2 = 0.9166666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.9166666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (x + -0.5) equal to 0.957427108 and -0.957427108.Subproblem 1
x + -0.5 = 0.957427108 Simplifying x + -0.5 = 0.957427108 Reorder the terms: -0.5 + x = 0.957427108 Solving -0.5 + x = 0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.957427108 + 0.5 x = 0.957427108 + 0.5 Combine like terms: 0.957427108 + 0.5 = 1.457427108 x = 1.457427108 Simplifying x = 1.457427108Subproblem 2
x + -0.5 = -0.957427108 Simplifying x + -0.5 = -0.957427108 Reorder the terms: -0.5 + x = -0.957427108 Solving -0.5 + x = -0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.957427108 + 0.5 x = -0.957427108 + 0.5 Combine like terms: -0.957427108 + 0.5 = -0.457427108 x = -0.457427108 Simplifying x = -0.457427108Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.457427108, -0.457427108}Solution
x = {1.457427108, -0.457427108}
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