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Simplifying (7x2 + 2x + -9) + -1(3x2 + 3x + 2) + (2x2 + -5) = 0 Reorder the terms: (-9 + 2x + 7x2) + -1(3x2 + 3x + 2) + (2x2 + -5) = 0 Remove parenthesis around (-9 + 2x + 7x2) -9 + 2x + 7x2 + -1(3x2 + 3x + 2) + (2x2 + -5) = 0 Reorder the terms: -9 + 2x + 7x2 + -1(2 + 3x + 3x2) + (2x2 + -5) = 0 -9 + 2x + 7x2 + (2 * -1 + 3x * -1 + 3x2 * -1) + (2x2 + -5) = 0 -9 + 2x + 7x2 + (-2 + -3x + -3x2) + (2x2 + -5) = 0 Reorder the terms: -9 + 2x + 7x2 + -2 + -3x + -3x2 + (-5 + 2x2) = 0 Remove parenthesis around (-5 + 2x2) -9 + 2x + 7x2 + -2 + -3x + -3x2 + -5 + 2x2 = 0 Reorder the terms: -9 + -2 + -5 + 2x + -3x + 7x2 + -3x2 + 2x2 = 0 Combine like terms: -9 + -2 = -11 -11 + -5 + 2x + -3x + 7x2 + -3x2 + 2x2 = 0 Combine like terms: -11 + -5 = -16 -16 + 2x + -3x + 7x2 + -3x2 + 2x2 = 0 Combine like terms: 2x + -3x = -1x -16 + -1x + 7x2 + -3x2 + 2x2 = 0 Combine like terms: 7x2 + -3x2 = 4x2 -16 + -1x + 4x2 + 2x2 = 0 Combine like terms: 4x2 + 2x2 = 6x2 -16 + -1x + 6x2 = 0 Solving -16 + -1x + 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'. -2.666666667 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -0.1666666667x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -0.1666666667x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -0.1666666667x + x2 = 0 + 2.666666667 -0.1666666667x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -0.1666666667x + x2 = 2.666666667 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 2.666666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 2.666666667 + 0.006944444447 Combine like terms: 2.666666667 + 0.006944444447 = 2.673611111447 0.006944444447 + -0.1666666667x + x2 = 2.673611111447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 2.673611111447 Calculate the square root of the right side: 1.635118073 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.635118073 and -1.635118073.Subproblem 1
x + -0.08333333335 = 1.635118073 Simplifying x + -0.08333333335 = 1.635118073 Reorder the terms: -0.08333333335 + x = 1.635118073 Solving -0.08333333335 + x = 1.635118073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 1.635118073 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.635118073 + 0.08333333335 x = 1.635118073 + 0.08333333335 Combine like terms: 1.635118073 + 0.08333333335 = 1.71845140635 x = 1.71845140635 Simplifying x = 1.71845140635Subproblem 2
x + -0.08333333335 = -1.635118073 Simplifying x + -0.08333333335 = -1.635118073 Reorder the terms: -0.08333333335 + x = -1.635118073 Solving -0.08333333335 + x = -1.635118073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -1.635118073 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.635118073 + 0.08333333335 x = -1.635118073 + 0.08333333335 Combine like terms: -1.635118073 + 0.08333333335 = -1.55178473965 x = -1.55178473965 Simplifying x = -1.55178473965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.71845140635, -1.55178473965}
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