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Simplifying 12x2 + -98x + 10 = 0 Reorder the terms: 10 + -98x + 12x2 = 0 Solving 10 + -98x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -49x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -49x + 6x2)' equal to zero and attempt to solve: Simplifying 5 + -49x + 6x2 = 0 Solving 5 + -49x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -8.166666667x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -8.166666667x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -8.166666667x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -8.166666667x + x2 = 0 + -0.8333333333 -8.166666667x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -8.166666667x + x2 = -0.8333333333 The x term is -8.166666667x. Take half its coefficient (-4.083333334). Square it (16.67361112) and add it to both sides. Add '16.67361112' to each side of the equation. -8.166666667x + 16.67361112 + x2 = -0.8333333333 + 16.67361112 Reorder the terms: 16.67361112 + -8.166666667x + x2 = -0.8333333333 + 16.67361112 Combine like terms: -0.8333333333 + 16.67361112 = 15.8402777867 16.67361112 + -8.166666667x + x2 = 15.8402777867 Factor a perfect square on the left side: (x + -4.083333334)(x + -4.083333334) = 15.8402777867 Calculate the square root of the right side: 3.979984647 Break this problem into two subproblems by setting (x + -4.083333334) equal to 3.979984647 and -3.979984647.Subproblem 1
x + -4.083333334 = 3.979984647 Simplifying x + -4.083333334 = 3.979984647 Reorder the terms: -4.083333334 + x = 3.979984647 Solving -4.083333334 + x = 3.979984647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.083333334' to each side of the equation. -4.083333334 + 4.083333334 + x = 3.979984647 + 4.083333334 Combine like terms: -4.083333334 + 4.083333334 = 0.000000000 0.000000000 + x = 3.979984647 + 4.083333334 x = 3.979984647 + 4.083333334 Combine like terms: 3.979984647 + 4.083333334 = 8.063317981 x = 8.063317981 Simplifying x = 8.063317981Subproblem 2
x + -4.083333334 = -3.979984647 Simplifying x + -4.083333334 = -3.979984647 Reorder the terms: -4.083333334 + x = -3.979984647 Solving -4.083333334 + x = -3.979984647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.083333334' to each side of the equation. -4.083333334 + 4.083333334 + x = -3.979984647 + 4.083333334 Combine like terms: -4.083333334 + 4.083333334 = 0.000000000 0.000000000 + x = -3.979984647 + 4.083333334 x = -3.979984647 + 4.083333334 Combine like terms: -3.979984647 + 4.083333334 = 0.103348687 x = 0.103348687 Simplifying x = 0.103348687Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.063317981, 0.103348687}Solution
x = {8.063317981, 0.103348687}
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