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Simplifying 3x2 + -48x + 4 = 0 Reorder the terms: 4 + -48x + 3x2 = 0 Solving 4 + -48x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -16x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -16x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -16x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -16x + x2 = 0 + -1.333333333 -16x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -16x + x2 = -1.333333333 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -1.333333333 + 64 Reorder the terms: 64 + -16x + x2 = -1.333333333 + 64 Combine like terms: -1.333333333 + 64 = 62.666666667 64 + -16x + x2 = 62.666666667 Factor a perfect square on the left side: (x + -8)(x + -8) = 62.666666667 Calculate the square root of the right side: 7.916228058 Break this problem into two subproblems by setting (x + -8) equal to 7.916228058 and -7.916228058.Subproblem 1
x + -8 = 7.916228058 Simplifying x + -8 = 7.916228058 Reorder the terms: -8 + x = 7.916228058 Solving -8 + x = 7.916228058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.916228058 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.916228058 + 8 x = 7.916228058 + 8 Combine like terms: 7.916228058 + 8 = 15.916228058 x = 15.916228058 Simplifying x = 15.916228058Subproblem 2
x + -8 = -7.916228058 Simplifying x + -8 = -7.916228058 Reorder the terms: -8 + x = -7.916228058 Solving -8 + x = -7.916228058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.916228058 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.916228058 + 8 x = -7.916228058 + 8 Combine like terms: -7.916228058 + 8 = 0.083771942 x = 0.083771942 Simplifying x = 0.083771942Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.916228058, 0.083771942}
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