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Simplifying (12x2) + -100x + 162 = 0 Reorder the terms: 162 + -100x + (12x2) = 0 Solving 162 + -100x + (12x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(81 + -50x + (6x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(81 + -50x + (6x2))' equal to zero and attempt to solve: Simplifying 81 + -50x + (6x2) = 0 Solving 81 + -50x + (6x2) = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 13.5 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -8.333333333x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -8.333333333x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -8.333333333x + x2 = 0 + -13.5 -8.333333333x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -8.333333333x + x2 = -13.5 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = -13.5 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = -13.5 + 17.36111111 Combine like terms: -13.5 + 17.36111111 = 3.86111111 17.36111111 + -8.333333333x + x2 = 3.86111111 Factor a perfect square on the left side: ((x) + -4.166666667)((x) + -4.166666667) = 3.86111111 Calculate the square root of the right side: 1.96497102 Break this problem into two subproblems by setting ((x) + -4.166666667) equal to 1.96497102 and -1.96497102.Subproblem 1
(x) + -4.166666667 = 1.96497102 Simplifying (x) + -4.166666667 = 1.96497102 x + -4.166666667 = 1.96497102 Reorder the terms: -4.166666667 + x = 1.96497102 Solving -4.166666667 + x = 1.96497102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 1.96497102 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 1.96497102 + 4.166666667 x = 1.96497102 + 4.166666667 Combine like terms: 1.96497102 + 4.166666667 = 6.131637687 x = 6.131637687 Simplifying x = 6.131637687Subproblem 2
(x) + -4.166666667 = -1.96497102 Simplifying (x) + -4.166666667 = -1.96497102 x + -4.166666667 = -1.96497102 Reorder the terms: -4.166666667 + x = -1.96497102 Solving -4.166666667 + x = -1.96497102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -1.96497102 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -1.96497102 + 4.166666667 x = -1.96497102 + 4.166666667 Combine like terms: -1.96497102 + 4.166666667 = 2.201695647 x = 2.201695647 Simplifying x = 2.201695647Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.131637687, 2.201695647}Solution
x = {6.131637687, 2.201695647}
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