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Simplifying 24x2 + -200x + 308 = 0 Reorder the terms: 308 + -200x + 24x2 = 0 Solving 308 + -200x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(77 + -50x + 6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(77 + -50x + 6x2)' equal to zero and attempt to solve: Simplifying 77 + -50x + 6x2 = 0 Solving 77 + -50x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 12.83333333 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '-12.83333333' to each side of the equation. 12.83333333 + -8.333333333x + -12.83333333 + x2 = 0 + -12.83333333 Reorder the terms: 12.83333333 + -12.83333333 + -8.333333333x + x2 = 0 + -12.83333333 Combine like terms: 12.83333333 + -12.83333333 = 0.00000000 0.00000000 + -8.333333333x + x2 = 0 + -12.83333333 -8.333333333x + x2 = 0 + -12.83333333 Combine like terms: 0 + -12.83333333 = -12.83333333 -8.333333333x + x2 = -12.83333333 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 = -12.83333333 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = -12.83333333 + 17.36111111 Combine like terms: -12.83333333 + 17.36111111 = 4.52777778 17.36111111 + -8.333333333x + x2 = 4.52777778 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 4.52777778 Calculate the square root of the right side: 2.127857556 Break this problem into two subproblems by setting (x + -4.166666667) equal to 2.127857556 and -2.127857556.Subproblem 1
x + -4.166666667 = 2.127857556 Simplifying x + -4.166666667 = 2.127857556 Reorder the terms: -4.166666667 + x = 2.127857556 Solving -4.166666667 + x = 2.127857556 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 = 2.127857556 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 2.127857556 + 4.166666667 x = 2.127857556 + 4.166666667 Combine like terms: 2.127857556 + 4.166666667 = 6.294524223 x = 6.294524223 Simplifying x = 6.294524223Subproblem 2
x + -4.166666667 = -2.127857556 Simplifying x + -4.166666667 = -2.127857556 Reorder the terms: -4.166666667 + x = -2.127857556 Solving -4.166666667 + x = -2.127857556 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 = -2.127857556 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -2.127857556 + 4.166666667 x = -2.127857556 + 4.166666667 Combine like terms: -2.127857556 + 4.166666667 = 2.038809111 x = 2.038809111 Simplifying x = 2.038809111Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.294524223, 2.038809111}Solution
x = {6.294524223, 2.038809111}
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