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Simplifying 9x2 + 2x + -4 = 26 Reorder the terms: -4 + 2x + 9x2 = 26 Solving -4 + 2x + 9x2 = 26 Solving for variable 'x'. Reorder the terms: -4 + -26 + 2x + 9x2 = 26 + -26 Combine like terms: -4 + -26 = -30 -30 + 2x + 9x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -30 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.333333333 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 0.2222222222x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 0.2222222222x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 3.333333333 0.2222222222x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 0.2222222222x + x2 = 3.333333333 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 = 3.333333333 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 3.333333333 + 0.01234567901 Combine like terms: 3.333333333 + 0.01234567901 = 3.34567901201 0.01234567901 + 0.2222222222x + x2 = 3.34567901201 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 3.34567901201 Calculate the square root of the right side: 1.829119737 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 1.829119737 and -1.829119737.Subproblem 1
x + 0.1111111111 = 1.829119737 Simplifying x + 0.1111111111 = 1.829119737 Reorder the terms: 0.1111111111 + x = 1.829119737 Solving 0.1111111111 + x = 1.829119737 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 = 1.829119737 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.829119737 + -0.1111111111 x = 1.829119737 + -0.1111111111 Combine like terms: 1.829119737 + -0.1111111111 = 1.7180086259 x = 1.7180086259 Simplifying x = 1.7180086259Subproblem 2
x + 0.1111111111 = -1.829119737 Simplifying x + 0.1111111111 = -1.829119737 Reorder the terms: 0.1111111111 + x = -1.829119737 Solving 0.1111111111 + x = -1.829119737 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 = -1.829119737 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.829119737 + -0.1111111111 x = -1.829119737 + -0.1111111111 Combine like terms: -1.829119737 + -0.1111111111 = -1.9402308481 x = -1.9402308481 Simplifying x = -1.9402308481Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7180086259, -1.9402308481}
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