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Simplifying (3x2 + -7x + 19) + (6x2 + 9x + -89) = 0 Reorder the terms: (19 + -7x + 3x2) + (6x2 + 9x + -89) = 0 Remove parenthesis around (19 + -7x + 3x2) 19 + -7x + 3x2 + (6x2 + 9x + -89) = 0 Reorder the terms: 19 + -7x + 3x2 + (-89 + 9x + 6x2) = 0 Remove parenthesis around (-89 + 9x + 6x2) 19 + -7x + 3x2 + -89 + 9x + 6x2 = 0 Reorder the terms: 19 + -89 + -7x + 9x + 3x2 + 6x2 = 0 Combine like terms: 19 + -89 = -70 -70 + -7x + 9x + 3x2 + 6x2 = 0 Combine like terms: -7x + 9x = 2x -70 + 2x + 3x2 + 6x2 = 0 Combine like terms: 3x2 + 6x2 = 9x2 -70 + 2x + 9x2 = 0 Solving -70 + 2x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -7.777777778 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '7.777777778' to each side of the equation. -7.777777778 + 0.2222222222x + 7.777777778 + x2 = 0 + 7.777777778 Reorder the terms: -7.777777778 + 7.777777778 + 0.2222222222x + x2 = 0 + 7.777777778 Combine like terms: -7.777777778 + 7.777777778 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 7.777777778 0.2222222222x + x2 = 0 + 7.777777778 Combine like terms: 0 + 7.777777778 = 7.777777778 0.2222222222x + x2 = 7.777777778 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 7.777777778 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 7.777777778 + 0.01234567901 Combine like terms: 7.777777778 + 0.01234567901 = 7.79012345701 0.01234567901 + 0.2222222222x + x2 = 7.79012345701 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 7.79012345701 Calculate the square root of the right side: 2.791079264 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 2.791079264 and -2.791079264.Subproblem 1
x + 0.1111111111 = 2.791079264 Simplifying x + 0.1111111111 = 2.791079264 Reorder the terms: 0.1111111111 + x = 2.791079264 Solving 0.1111111111 + x = 2.791079264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 2.791079264 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 2.791079264 + -0.1111111111 x = 2.791079264 + -0.1111111111 Combine like terms: 2.791079264 + -0.1111111111 = 2.6799681529 x = 2.6799681529 Simplifying x = 2.6799681529Subproblem 2
x + 0.1111111111 = -2.791079264 Simplifying x + 0.1111111111 = -2.791079264 Reorder the terms: 0.1111111111 + x = -2.791079264 Solving 0.1111111111 + x = -2.791079264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -2.791079264 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -2.791079264 + -0.1111111111 x = -2.791079264 + -0.1111111111 Combine like terms: -2.791079264 + -0.1111111111 = -2.9021903751 x = -2.9021903751 Simplifying x = -2.9021903751Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6799681529, -2.9021903751}
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