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Simplifying 128 + -96x + 12x2 = 0 Solving 128 + -96x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(32 + -24x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(32 + -24x + 3x2)' equal to zero and attempt to solve: Simplifying 32 + -24x + 3x2 = 0 Solving 32 + -24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.66666667 + -8x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + -8x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + -8x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + -8x + x2 = 0 + -10.66666667 -8x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 -8x + x2 = -10.66666667 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 = -10.66666667 + 16 Reorder the terms: 16 + -8x + x2 = -10.66666667 + 16 Combine like terms: -10.66666667 + 16 = 5.33333333 16 + -8x + x2 = 5.33333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 5.33333333 Calculate the square root of the right side: 2.309401076 Break this problem into two subproblems by setting (x + -4) equal to 2.309401076 and -2.309401076.Subproblem 1
x + -4 = 2.309401076 Simplifying x + -4 = 2.309401076 Reorder the terms: -4 + x = 2.309401076 Solving -4 + x = 2.309401076 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 = 2.309401076 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.309401076 + 4 x = 2.309401076 + 4 Combine like terms: 2.309401076 + 4 = 6.309401076 x = 6.309401076 Simplifying x = 6.309401076Subproblem 2
x + -4 = -2.309401076 Simplifying x + -4 = -2.309401076 Reorder the terms: -4 + x = -2.309401076 Solving -4 + x = -2.309401076 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 = -2.309401076 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.309401076 + 4 x = -2.309401076 + 4 Combine like terms: -2.309401076 + 4 = 1.690598924 x = 1.690598924 Simplifying x = 1.690598924Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.309401076, 1.690598924}Solution
x = {6.309401076, 1.690598924}
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