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Simplifying 0 = 12x2 + -96x + 14 Reorder the terms: 0 = 14 + -96x + 12x2 Solving 0 = 14 + -96x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -14 = -14 -14 + 96x + -12x2 = 14 + -96x + 12x2 + -14 + 96x + -12x2 Reorder the terms: -14 + 96x + -12x2 = 14 + -14 + -96x + 96x + 12x2 + -12x2 Combine like terms: 14 + -14 = 0 -14 + 96x + -12x2 = 0 + -96x + 96x + 12x2 + -12x2 -14 + 96x + -12x2 = -96x + 96x + 12x2 + -12x2 Combine like terms: -96x + 96x = 0 -14 + 96x + -12x2 = 0 + 12x2 + -12x2 -14 + 96x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -14 + 96x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 48x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 48x + -6x2)' equal to zero and attempt to solve: Simplifying -7 + 48x + -6x2 = 0 Solving -7 + 48x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 1.166666667 + -8x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + -8x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + -8x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + -8x + x2 = 0 + -1.166666667 -8x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 -8x + x2 = -1.166666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -1.166666667 + 16 Reorder the terms: 16 + -8x + x2 = -1.166666667 + 16 Combine like terms: -1.166666667 + 16 = 14.833333333 16 + -8x + x2 = 14.833333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 14.833333333 Calculate the square root of the right side: 3.851406669 Break this problem into two subproblems by setting (x + -4) equal to 3.851406669 and -3.851406669.Subproblem 1
x + -4 = 3.851406669 Simplifying x + -4 = 3.851406669 Reorder the terms: -4 + x = 3.851406669 Solving -4 + x = 3.851406669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.851406669 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.851406669 + 4 x = 3.851406669 + 4 Combine like terms: 3.851406669 + 4 = 7.851406669 x = 7.851406669 Simplifying x = 7.851406669Subproblem 2
x + -4 = -3.851406669 Simplifying x + -4 = -3.851406669 Reorder the terms: -4 + x = -3.851406669 Solving -4 + x = -3.851406669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.851406669 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.851406669 + 4 x = -3.851406669 + 4 Combine like terms: -3.851406669 + 4 = 0.148593331 x = 0.148593331 Simplifying x = 0.148593331Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.851406669, 0.148593331}Solution
x = {7.851406669, 0.148593331}
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