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Simplifying 12x2 + -168x + 405 = 0 Reorder the terms: 405 + -168x + 12x2 = 0 Solving 405 + -168x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(135 + -56x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(135 + -56x + 4x2)' equal to zero and attempt to solve: Simplifying 135 + -56x + 4x2 = 0 Solving 135 + -56x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 33.75 + -14x + x2 = 0 Move the constant term to the right: Add '-33.75' to each side of the equation. 33.75 + -14x + -33.75 + x2 = 0 + -33.75 Reorder the terms: 33.75 + -33.75 + -14x + x2 = 0 + -33.75 Combine like terms: 33.75 + -33.75 = 0.00 0.00 + -14x + x2 = 0 + -33.75 -14x + x2 = 0 + -33.75 Combine like terms: 0 + -33.75 = -33.75 -14x + x2 = -33.75 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -33.75 + 49 Reorder the terms: 49 + -14x + x2 = -33.75 + 49 Combine like terms: -33.75 + 49 = 15.25 49 + -14x + x2 = 15.25 Factor a perfect square on the left side: (x + -7)(x + -7) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -7) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -7 = 3.905124838 Simplifying x + -7 = 3.905124838 Reorder the terms: -7 + x = 3.905124838 Solving -7 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 3.905124838 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.905124838 + 7 x = 3.905124838 + 7 Combine like terms: 3.905124838 + 7 = 10.905124838 x = 10.905124838 Simplifying x = 10.905124838Subproblem 2
x + -7 = -3.905124838 Simplifying x + -7 = -3.905124838 Reorder the terms: -7 + x = -3.905124838 Solving -7 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -3.905124838 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.905124838 + 7 x = -3.905124838 + 7 Combine like terms: -3.905124838 + 7 = 3.094875162 x = 3.094875162 Simplifying x = 3.094875162Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.905124838, 3.094875162}Solution
x = {10.905124838, 3.094875162}
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