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Simplifying -36x2 + 8x + 98 = 0 Reorder the terms: 98 + 8x + -36x2 = 0 Solving 98 + 8x + -36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(49 + 4x + -18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + 4x + -18x2)' equal to zero and attempt to solve: Simplifying 49 + 4x + -18x2 = 0 Solving 49 + 4x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -2.722222222 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '2.722222222' to each side of the equation. -2.722222222 + -0.2222222222x + 2.722222222 + x2 = 0 + 2.722222222 Reorder the terms: -2.722222222 + 2.722222222 + -0.2222222222x + x2 = 0 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + -0.2222222222x + x2 = 0 + 2.722222222 -0.2222222222x + x2 = 0 + 2.722222222 Combine like terms: 0 + 2.722222222 = 2.722222222 -0.2222222222x + x2 = 2.722222222 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 = 2.722222222 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 2.722222222 + 0.01234567901 Combine like terms: 2.722222222 + 0.01234567901 = 2.73456790101 0.01234567901 + -0.2222222222x + x2 = 2.73456790101 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 2.73456790101 Calculate the square root of the right side: 1.653652896 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 1.653652896 and -1.653652896.Subproblem 1
x + -0.1111111111 = 1.653652896 Simplifying x + -0.1111111111 = 1.653652896 Reorder the terms: -0.1111111111 + x = 1.653652896 Solving -0.1111111111 + x = 1.653652896 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 = 1.653652896 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 1.653652896 + 0.1111111111 x = 1.653652896 + 0.1111111111 Combine like terms: 1.653652896 + 0.1111111111 = 1.7647640071 x = 1.7647640071 Simplifying x = 1.7647640071Subproblem 2
x + -0.1111111111 = -1.653652896 Simplifying x + -0.1111111111 = -1.653652896 Reorder the terms: -0.1111111111 + x = -1.653652896 Solving -0.1111111111 + x = -1.653652896 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 = -1.653652896 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -1.653652896 + 0.1111111111 x = -1.653652896 + 0.1111111111 Combine like terms: -1.653652896 + 0.1111111111 = -1.5425417849 x = -1.5425417849 Simplifying x = -1.5425417849Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7647640071, -1.5425417849}Solution
x = {1.7647640071, -1.5425417849}
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