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Simplifying 9x2 + 10x + 28 = 26 Reorder the terms: 28 + 10x + 9x2 = 26 Solving 28 + 10x + 9x2 = 26 Solving for variable 'x'. Reorder the terms: 28 + -26 + 10x + 9x2 = 26 + -26 Combine like terms: 28 + -26 = 2 2 + 10x + 9x2 = 26 + -26 Combine like terms: 26 + -26 = 0 2 + 10x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 1.111111111x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 1.111111111x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 1.111111111x + x2 = 0 + -0.2222222222 1.111111111x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 1.111111111x + x2 = -0.2222222222 The x term is 1.111111111x. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x + 0.3086419752 + x2 = -0.2222222222 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = -0.2222222222 + 0.3086419752 Combine like terms: -0.2222222222 + 0.3086419752 = 0.086419753 0.3086419752 + 1.111111111x + x2 = 0.086419753 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 0.086419753 Calculate the square root of the right side: 0.293972368 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 0.293972368 and -0.293972368.Subproblem 1
x + 0.5555555555 = 0.293972368 Simplifying x + 0.5555555555 = 0.293972368 Reorder the terms: 0.5555555555 + x = 0.293972368 Solving 0.5555555555 + x = 0.293972368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 0.293972368 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 0.293972368 + -0.5555555555 x = 0.293972368 + -0.5555555555 Combine like terms: 0.293972368 + -0.5555555555 = -0.2615831875 x = -0.2615831875 Simplifying x = -0.2615831875Subproblem 2
x + 0.5555555555 = -0.293972368 Simplifying x + 0.5555555555 = -0.293972368 Reorder the terms: 0.5555555555 + x = -0.293972368 Solving 0.5555555555 + x = -0.293972368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -0.293972368 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -0.293972368 + -0.5555555555 x = -0.293972368 + -0.5555555555 Combine like terms: -0.293972368 + -0.5555555555 = -0.8495279235 x = -0.8495279235 Simplifying x = -0.8495279235Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2615831875, -0.8495279235}
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