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Simplifying (9x2 + 9x + 4) + -1(3x2 + 8) = 0 Reorder the terms: (4 + 9x + 9x2) + -1(3x2 + 8) = 0 Remove parenthesis around (4 + 9x + 9x2) 4 + 9x + 9x2 + -1(3x2 + 8) = 0 Reorder the terms: 4 + 9x + 9x2 + -1(8 + 3x2) = 0 4 + 9x + 9x2 + (8 * -1 + 3x2 * -1) = 0 4 + 9x + 9x2 + (-8 + -3x2) = 0 Reorder the terms: 4 + -8 + 9x + 9x2 + -3x2 = 0 Combine like terms: 4 + -8 = -4 -4 + 9x + 9x2 + -3x2 = 0 Combine like terms: 9x2 + -3x2 = 6x2 -4 + 9x + 6x2 = 0 Solving -4 + 9x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.6666666667 + 1.5x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 1.5x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 1.5x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 1.5x + x2 = 0 + 0.6666666667 1.5x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 1.5x + x2 = 0.6666666667 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 0.6666666667 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.6666666667 + 0.5625 Combine like terms: 0.6666666667 + 0.5625 = 1.2291666667 0.5625 + 1.5x + x2 = 1.2291666667 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.2291666667 Calculate the square root of the right side: 1.108677891 Break this problem into two subproblems by setting (x + 0.75) equal to 1.108677891 and -1.108677891.Subproblem 1
x + 0.75 = 1.108677891 Simplifying x + 0.75 = 1.108677891 Reorder the terms: 0.75 + x = 1.108677891 Solving 0.75 + x = 1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.108677891 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.108677891 + -0.75 x = 1.108677891 + -0.75 Combine like terms: 1.108677891 + -0.75 = 0.358677891 x = 0.358677891 Simplifying x = 0.358677891Subproblem 2
x + 0.75 = -1.108677891 Simplifying x + 0.75 = -1.108677891 Reorder the terms: 0.75 + x = -1.108677891 Solving 0.75 + x = -1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.108677891 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.108677891 + -0.75 x = -1.108677891 + -0.75 Combine like terms: -1.108677891 + -0.75 = -1.858677891 x = -1.858677891 Simplifying x = -1.858677891Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.358677891, -1.858677891}
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