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Simplifying 144x2 + 732x + -36 = 0 Reorder the terms: -36 + 732x + 144x2 = 0 Solving -36 + 732x + 144x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-3 + 61x + 12x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-3 + 61x + 12x2)' equal to zero and attempt to solve: Simplifying -3 + 61x + 12x2 = 0 Solving -3 + 61x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.25 + 5.083333333x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 5.083333333x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 5.083333333x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 5.083333333x + x2 = 0 + 0.25 5.083333333x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 5.083333333x + x2 = 0.25 The x term is 5.083333333x. Take half its coefficient (2.541666667). Square it (6.460069446) and add it to both sides. Add '6.460069446' to each side of the equation. 5.083333333x + 6.460069446 + x2 = 0.25 + 6.460069446 Reorder the terms: 6.460069446 + 5.083333333x + x2 = 0.25 + 6.460069446 Combine like terms: 0.25 + 6.460069446 = 6.710069446 6.460069446 + 5.083333333x + x2 = 6.710069446 Factor a perfect square on the left side: (x + 2.541666667)(x + 2.541666667) = 6.710069446 Calculate the square root of the right side: 2.590380174 Break this problem into two subproblems by setting (x + 2.541666667) equal to 2.590380174 and -2.590380174.Subproblem 1
x + 2.541666667 = 2.590380174 Simplifying x + 2.541666667 = 2.590380174 Reorder the terms: 2.541666667 + x = 2.590380174 Solving 2.541666667 + x = 2.590380174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.541666667' to each side of the equation. 2.541666667 + -2.541666667 + x = 2.590380174 + -2.541666667 Combine like terms: 2.541666667 + -2.541666667 = 0.000000000 0.000000000 + x = 2.590380174 + -2.541666667 x = 2.590380174 + -2.541666667 Combine like terms: 2.590380174 + -2.541666667 = 0.048713507 x = 0.048713507 Simplifying x = 0.048713507Subproblem 2
x + 2.541666667 = -2.590380174 Simplifying x + 2.541666667 = -2.590380174 Reorder the terms: 2.541666667 + x = -2.590380174 Solving 2.541666667 + x = -2.590380174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.541666667' to each side of the equation. 2.541666667 + -2.541666667 + x = -2.590380174 + -2.541666667 Combine like terms: 2.541666667 + -2.541666667 = 0.000000000 0.000000000 + x = -2.590380174 + -2.541666667 x = -2.590380174 + -2.541666667 Combine like terms: -2.590380174 + -2.541666667 = -5.132046841 x = -5.132046841 Simplifying x = -5.132046841Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.048713507, -5.132046841}Solution
x = {0.048713507, -5.132046841}
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