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Simplifying 6x2 + -48x + 8 = 4 Reorder the terms: 8 + -48x + 6x2 = 4 Solving 8 + -48x + 6x2 = 4 Solving for variable 'x'. Reorder the terms: 8 + -4 + -48x + 6x2 = 4 + -4 Combine like terms: 8 + -4 = 4 4 + -48x + 6x2 = 4 + -4 Combine like terms: 4 + -4 = 0 4 + -48x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -24x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -24x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + -24x + 3x2 = 0 Solving 2 + -24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -8x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -8x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -8x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -8x + x2 = 0 + -0.6666666667 -8x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -8x + x2 = -0.6666666667 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 = -0.6666666667 + 16 Reorder the terms: 16 + -8x + x2 = -0.6666666667 + 16 Combine like terms: -0.6666666667 + 16 = 15.3333333333 16 + -8x + x2 = 15.3333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.3333333333 Calculate the square root of the right side: 3.915780041 Break this problem into two subproblems by setting (x + -4) equal to 3.915780041 and -3.915780041.Subproblem 1
x + -4 = 3.915780041 Simplifying x + -4 = 3.915780041 Reorder the terms: -4 + x = 3.915780041 Solving -4 + x = 3.915780041 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 = 3.915780041 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.915780041 + 4 x = 3.915780041 + 4 Combine like terms: 3.915780041 + 4 = 7.915780041 x = 7.915780041 Simplifying x = 7.915780041Subproblem 2
x + -4 = -3.915780041 Simplifying x + -4 = -3.915780041 Reorder the terms: -4 + x = -3.915780041 Solving -4 + x = -3.915780041 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 = -3.915780041 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.915780041 + 4 x = -3.915780041 + 4 Combine like terms: -3.915780041 + 4 = 0.084219959 x = 0.084219959 Simplifying x = 0.084219959Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.915780041, 0.084219959}Solution
x = {7.915780041, 0.084219959}
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