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Simplifying 3x2 + -48x + 16 = 0 Reorder the terms: 16 + -48x + 3x2 = 0 Solving 16 + -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'. 5.333333333 + -16x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -16x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -16x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -16x + x2 = 0 + -5.333333333 -16x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -16x + x2 = -5.333333333 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 = -5.333333333 + 64 Reorder the terms: 64 + -16x + x2 = -5.333333333 + 64 Combine like terms: -5.333333333 + 64 = 58.666666667 64 + -16x + x2 = 58.666666667 Factor a perfect square on the left side: (x + -8)(x + -8) = 58.666666667 Calculate the square root of the right side: 7.659416862 Break this problem into two subproblems by setting (x + -8) equal to 7.659416862 and -7.659416862.Subproblem 1
x + -8 = 7.659416862 Simplifying x + -8 = 7.659416862 Reorder the terms: -8 + x = 7.659416862 Solving -8 + x = 7.659416862 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 = 7.659416862 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.659416862 + 8 x = 7.659416862 + 8 Combine like terms: 7.659416862 + 8 = 15.659416862 x = 15.659416862 Simplifying x = 15.659416862Subproblem 2
x + -8 = -7.659416862 Simplifying x + -8 = -7.659416862 Reorder the terms: -8 + x = -7.659416862 Solving -8 + x = -7.659416862 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 = -7.659416862 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.659416862 + 8 x = -7.659416862 + 8 Combine like terms: -7.659416862 + 8 = 0.340583138 x = 0.340583138 Simplifying x = 0.340583138Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.659416862, 0.340583138}
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