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Simplifying (36x2) + -120x = -70 Reorder the terms: -120x + (36x2) = -70 Solving -120x + (36x2) = -70 Solving for variable 'x'. Reorder the terms: 70 + -120x + (36x2) = -70 + 70 Combine like terms: -70 + 70 = 0 70 + -120x + (36x2) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(35 + -60x + (18x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + -60x + (18x2))' equal to zero and attempt to solve: Simplifying 35 + -60x + (18x2) = 0 Solving 35 + -60x + (18x2) = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 1.944444444 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-1.944444444' to each side of the equation. 1.944444444 + -3.333333333x + -1.944444444 + x2 = 0 + -1.944444444 Reorder the terms: 1.944444444 + -1.944444444 + -3.333333333x + x2 = 0 + -1.944444444 Combine like terms: 1.944444444 + -1.944444444 = 0.000000000 0.000000000 + -3.333333333x + x2 = 0 + -1.944444444 -3.333333333x + x2 = 0 + -1.944444444 Combine like terms: 0 + -1.944444444 = -1.944444444 -3.333333333x + x2 = -1.944444444 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -1.944444444 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -1.944444444 + 2.777777779 Combine like terms: -1.944444444 + 2.777777779 = 0.833333335 2.777777779 + -3.333333333x + x2 = 0.833333335 Factor a perfect square on the left side: ((x) + -1.666666667)((x) + -1.666666667) = 0.833333335 Calculate the square root of the right side: 0.91287093 Break this problem into two subproblems by setting ((x) + -1.666666667) equal to 0.91287093 and -0.91287093.Subproblem 1
(x) + -1.666666667 = 0.91287093 Simplifying (x) + -1.666666667 = 0.91287093 x + -1.666666667 = 0.91287093 Reorder the terms: -1.666666667 + x = 0.91287093 Solving -1.666666667 + x = 0.91287093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 0.91287093 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 0.91287093 + 1.666666667 x = 0.91287093 + 1.666666667 Combine like terms: 0.91287093 + 1.666666667 = 2.579537597 x = 2.579537597 Simplifying x = 2.579537597Subproblem 2
(x) + -1.666666667 = -0.91287093 Simplifying (x) + -1.666666667 = -0.91287093 x + -1.666666667 = -0.91287093 Reorder the terms: -1.666666667 + x = -0.91287093 Solving -1.666666667 + x = -0.91287093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -0.91287093 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -0.91287093 + 1.666666667 x = -0.91287093 + 1.666666667 Combine like terms: -0.91287093 + 1.666666667 = 0.753795737 x = 0.753795737 Simplifying x = 0.753795737Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.579537597, 0.753795737}Solution
x = {2.579537597, 0.753795737}
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