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Simplifying 2x(6x + 20) = 90 Reorder the terms: 2x(20 + 6x) = 90 (20 * 2x + 6x * 2x) = 90 (40x + 12x2) = 90 Solving 40x + 12x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 40x + 12x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 40x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 20x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + 20x + 6x2)' equal to zero and attempt to solve: Simplifying -45 + 20x + 6x2 = 0 Solving -45 + 20x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -7.5 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 3.333333333x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 3.333333333x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 3.333333333x + x2 = 0 + 7.5 3.333333333x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 3.333333333x + x2 = 7.5 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 = 7.5 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 7.5 + 2.777777779 Combine like terms: 7.5 + 2.777777779 = 10.277777779 2.777777779 + 3.333333333x + x2 = 10.277777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 10.277777779 Calculate the square root of the right side: 3.205897344 Break this problem into two subproblems by setting (x + 1.666666667) equal to 3.205897344 and -3.205897344.Subproblem 1
x + 1.666666667 = 3.205897344 Simplifying x + 1.666666667 = 3.205897344 Reorder the terms: 1.666666667 + x = 3.205897344 Solving 1.666666667 + x = 3.205897344 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 = 3.205897344 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 3.205897344 + -1.666666667 x = 3.205897344 + -1.666666667 Combine like terms: 3.205897344 + -1.666666667 = 1.539230677 x = 1.539230677 Simplifying x = 1.539230677Subproblem 2
x + 1.666666667 = -3.205897344 Simplifying x + 1.666666667 = -3.205897344 Reorder the terms: 1.666666667 + x = -3.205897344 Solving 1.666666667 + x = -3.205897344 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 = -3.205897344 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -3.205897344 + -1.666666667 x = -3.205897344 + -1.666666667 Combine like terms: -3.205897344 + -1.666666667 = -4.872564011 x = -4.872564011 Simplifying x = -4.872564011Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.539230677, -4.872564011}Solution
x = {1.539230677, -4.872564011}
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