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Simplifying 9x2 + -2x + -70 = 0 Reorder the terms: -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 = 2.9021903751 x = 2.9021903751 Simplifying x = 2.9021903751Subproblem 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 = -2.6799681529 x = -2.6799681529 Simplifying x = -2.6799681529Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9021903751, -2.6799681529}
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