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Simplifying 12x2 + -140x + 350 = 0 Reorder the terms: 350 + -140x + 12x2 = 0 Solving 350 + -140x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(175 + -70x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(175 + -70x + 6x2)' equal to zero and attempt to solve: Simplifying 175 + -70x + 6x2 = 0 Solving 175 + -70x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 29.16666667 + -11.66666667x + x2 = 0 Move the constant term to the right: Add '-29.16666667' to each side of the equation. 29.16666667 + -11.66666667x + -29.16666667 + x2 = 0 + -29.16666667 Reorder the terms: 29.16666667 + -29.16666667 + -11.66666667x + x2 = 0 + -29.16666667 Combine like terms: 29.16666667 + -29.16666667 = 0.00000000 0.00000000 + -11.66666667x + x2 = 0 + -29.16666667 -11.66666667x + x2 = 0 + -29.16666667 Combine like terms: 0 + -29.16666667 = -29.16666667 -11.66666667x + x2 = -29.16666667 The x term is -11.66666667x. Take half its coefficient (-5.833333335). Square it (34.02777780) and add it to both sides. Add '34.02777780' to each side of the equation. -11.66666667x + 34.02777780 + x2 = -29.16666667 + 34.02777780 Reorder the terms: 34.02777780 + -11.66666667x + x2 = -29.16666667 + 34.02777780 Combine like terms: -29.16666667 + 34.02777780 = 4.86111113 34.02777780 + -11.66666667x + x2 = 4.86111113 Factor a perfect square on the left side: (x + -5.833333335)(x + -5.833333335) = 4.86111113 Calculate the square root of the right side: 2.204792764 Break this problem into two subproblems by setting (x + -5.833333335) equal to 2.204792764 and -2.204792764.Subproblem 1
x + -5.833333335 = 2.204792764 Simplifying x + -5.833333335 = 2.204792764 Reorder the terms: -5.833333335 + x = 2.204792764 Solving -5.833333335 + x = 2.204792764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = 2.204792764 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = 2.204792764 + 5.833333335 x = 2.204792764 + 5.833333335 Combine like terms: 2.204792764 + 5.833333335 = 8.038126099 x = 8.038126099 Simplifying x = 8.038126099Subproblem 2
x + -5.833333335 = -2.204792764 Simplifying x + -5.833333335 = -2.204792764 Reorder the terms: -5.833333335 + x = -2.204792764 Solving -5.833333335 + x = -2.204792764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = -2.204792764 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = -2.204792764 + 5.833333335 x = -2.204792764 + 5.833333335 Combine like terms: -2.204792764 + 5.833333335 = 3.628540571 x = 3.628540571 Simplifying x = 3.628540571Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.038126099, 3.628540571}Solution
x = {8.038126099, 3.628540571}
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