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Simplifying 9x2 + 10x = 2 Reorder the terms: 10x + 9x2 = 2 Solving 10x + 9x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 10x + 9x2 = 2 + -2 Combine like terms: 2 + -2 = 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 = 0.5308641974 0.3086419752 + 1.111111111x + x2 = 0.5308641974 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 0.5308641974 Calculate the square root of the right side: 0.72860428 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 0.72860428 and -0.72860428.Subproblem 1
x + 0.5555555555 = 0.72860428 Simplifying x + 0.5555555555 = 0.72860428 Reorder the terms: 0.5555555555 + x = 0.72860428 Solving 0.5555555555 + x = 0.72860428 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 = 0.72860428 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 0.72860428 + -0.5555555555 x = 0.72860428 + -0.5555555555 Combine like terms: 0.72860428 + -0.5555555555 = 0.1730487245 x = 0.1730487245 Simplifying x = 0.1730487245Subproblem 2
x + 0.5555555555 = -0.72860428 Simplifying x + 0.5555555555 = -0.72860428 Reorder the terms: 0.5555555555 + x = -0.72860428 Solving 0.5555555555 + x = -0.72860428 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 = -0.72860428 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -0.72860428 + -0.5555555555 x = -0.72860428 + -0.5555555555 Combine like terms: -0.72860428 + -0.5555555555 = -1.2841598355 x = -1.2841598355 Simplifying x = -1.2841598355Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1730487245, -1.2841598355}
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