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Simplifying 456x2 + 5646x + 4 = 0 Reorder the terms: 4 + 5646x + 456x2 = 0 Solving 4 + 5646x + 456x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 2823x + 228x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 2823x + 228x2)' equal to zero and attempt to solve: Simplifying 2 + 2823x + 228x2 = 0 Solving 2 + 2823x + 228x2 = 0 Begin completing the square. Divide all terms by 228 the coefficient of the squared term: Divide each side by '228'. 0.008771929825 + 12.38157895x + x2 = 0 Move the constant term to the right: Add '-0.008771929825' to each side of the equation. 0.008771929825 + 12.38157895x + -0.008771929825 + x2 = 0 + -0.008771929825 Reorder the terms: 0.008771929825 + -0.008771929825 + 12.38157895x + x2 = 0 + -0.008771929825 Combine like terms: 0.008771929825 + -0.008771929825 = 0.000000000000 0.000000000000 + 12.38157895x + x2 = 0 + -0.008771929825 12.38157895x + x2 = 0 + -0.008771929825 Combine like terms: 0 + -0.008771929825 = -0.008771929825 12.38157895x + x2 = -0.008771929825 The x term is 12.38157895x. Take half its coefficient (6.190789475). Square it (38.32587432) and add it to both sides. Add '38.32587432' to each side of the equation. 12.38157895x + 38.32587432 + x2 = -0.008771929825 + 38.32587432 Reorder the terms: 38.32587432 + 12.38157895x + x2 = -0.008771929825 + 38.32587432 Combine like terms: -0.008771929825 + 38.32587432 = 38.317102390175 38.32587432 + 12.38157895x + x2 = 38.317102390175 Factor a perfect square on the left side: (x + 6.190789475)(x + 6.190789475) = 38.317102390175 Calculate the square root of the right side: 6.190080968 Break this problem into two subproblems by setting (x + 6.190789475) equal to 6.190080968 and -6.190080968.Subproblem 1
x + 6.190789475 = 6.190080968 Simplifying x + 6.190789475 = 6.190080968 Reorder the terms: 6.190789475 + x = 6.190080968 Solving 6.190789475 + x = 6.190080968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.190789475' to each side of the equation. 6.190789475 + -6.190789475 + x = 6.190080968 + -6.190789475 Combine like terms: 6.190789475 + -6.190789475 = 0.000000000 0.000000000 + x = 6.190080968 + -6.190789475 x = 6.190080968 + -6.190789475 Combine like terms: 6.190080968 + -6.190789475 = -0.000708507 x = -0.000708507 Simplifying x = -0.000708507Subproblem 2
x + 6.190789475 = -6.190080968 Simplifying x + 6.190789475 = -6.190080968 Reorder the terms: 6.190789475 + x = -6.190080968 Solving 6.190789475 + x = -6.190080968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.190789475' to each side of the equation. 6.190789475 + -6.190789475 + x = -6.190080968 + -6.190789475 Combine like terms: 6.190789475 + -6.190789475 = 0.000000000 0.000000000 + x = -6.190080968 + -6.190789475 x = -6.190080968 + -6.190789475 Combine like terms: -6.190080968 + -6.190789475 = -12.380870443 x = -12.380870443 Simplifying x = -12.380870443Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.000708507, -12.380870443}Solution
x = {-0.000708507, -12.380870443}
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