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Simplifying 18x2 + 4x = 56 Reorder the terms: 4x + 18x2 = 56 Solving 4x + 18x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + 4x + 18x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 4x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + 2x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + 2x + 9x2)' equal to zero and attempt to solve: Simplifying -28 + 2x + 9x2 = 0 Solving -28 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + 0.2222222222x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + 0.2222222222x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 3.111111111 0.2222222222x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 0.2222222222x + x2 = 3.111111111 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 = 3.111111111 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 3.111111111 + 0.01234567901 Combine like terms: 3.111111111 + 0.01234567901 = 3.12345679001 0.01234567901 + 0.2222222222x + x2 = 3.12345679001 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 3.12345679001 Calculate the square root of the right side: 1.767330413 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 1.767330413 and -1.767330413.Subproblem 1
x + 0.1111111111 = 1.767330413 Simplifying x + 0.1111111111 = 1.767330413 Reorder the terms: 0.1111111111 + x = 1.767330413 Solving 0.1111111111 + x = 1.767330413 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 = 1.767330413 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.767330413 + -0.1111111111 x = 1.767330413 + -0.1111111111 Combine like terms: 1.767330413 + -0.1111111111 = 1.6562193019 x = 1.6562193019 Simplifying x = 1.6562193019Subproblem 2
x + 0.1111111111 = -1.767330413 Simplifying x + 0.1111111111 = -1.767330413 Reorder the terms: 0.1111111111 + x = -1.767330413 Solving 0.1111111111 + x = -1.767330413 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 = -1.767330413 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.767330413 + -0.1111111111 x = -1.767330413 + -0.1111111111 Combine like terms: -1.767330413 + -0.1111111111 = -1.8784415241 x = -1.8784415241 Simplifying x = -1.8784415241Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6562193019, -1.8784415241}Solution
x = {1.6562193019, -1.8784415241}
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