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Simplifying (902 + -252x + 12x2) = 0 Remove parenthesis around (902 + -252x + 12x2) 902 + -252x + 12x2 = 0 Solving 902 + -252x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(451 + -126x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(451 + -126x + 6x2)' equal to zero and attempt to solve: Simplifying 451 + -126x + 6x2 = 0 Solving 451 + -126x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 75.16666667 + -21x + x2 = 0 Move the constant term to the right: Add '-75.16666667' to each side of the equation. 75.16666667 + -21x + -75.16666667 + x2 = 0 + -75.16666667 Reorder the terms: 75.16666667 + -75.16666667 + -21x + x2 = 0 + -75.16666667 Combine like terms: 75.16666667 + -75.16666667 = 0.00000000 0.00000000 + -21x + x2 = 0 + -75.16666667 -21x + x2 = 0 + -75.16666667 Combine like terms: 0 + -75.16666667 = -75.16666667 -21x + x2 = -75.16666667 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -75.16666667 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -75.16666667 + 110.25 Combine like terms: -75.16666667 + 110.25 = 35.08333333 110.25 + -21x + x2 = 35.08333333 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 35.08333333 Calculate the square root of the right side: 5.923118548 Break this problem into two subproblems by setting (x + -10.5) equal to 5.923118548 and -5.923118548.Subproblem 1
x + -10.5 = 5.923118548 Simplifying x + -10.5 = 5.923118548 Reorder the terms: -10.5 + x = 5.923118548 Solving -10.5 + x = 5.923118548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 5.923118548 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 5.923118548 + 10.5 x = 5.923118548 + 10.5 Combine like terms: 5.923118548 + 10.5 = 16.423118548 x = 16.423118548 Simplifying x = 16.423118548Subproblem 2
x + -10.5 = -5.923118548 Simplifying x + -10.5 = -5.923118548 Reorder the terms: -10.5 + x = -5.923118548 Solving -10.5 + x = -5.923118548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -5.923118548 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -5.923118548 + 10.5 x = -5.923118548 + 10.5 Combine like terms: -5.923118548 + 10.5 = 4.576881452 x = 4.576881452 Simplifying x = 4.576881452Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.423118548, 4.576881452}Solution
x = {16.423118548, 4.576881452}
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