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Simplifying 3x2 + -48x + -64 = 0 Reorder the terms: -64 + -48x + 3x2 = 0 Solving -64 + -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'. -21.33333333 + -16x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + -16x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + -16x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + -16x + x2 = 0 + 21.33333333 -16x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 -16x + x2 = 21.33333333 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 = 21.33333333 + 64 Reorder the terms: 64 + -16x + x2 = 21.33333333 + 64 Combine like terms: 21.33333333 + 64 = 85.33333333 64 + -16x + x2 = 85.33333333 Factor a perfect square on the left side: (x + -8)(x + -8) = 85.33333333 Calculate the square root of the right side: 9.237604307 Break this problem into two subproblems by setting (x + -8) equal to 9.237604307 and -9.237604307.Subproblem 1
x + -8 = 9.237604307 Simplifying x + -8 = 9.237604307 Reorder the terms: -8 + x = 9.237604307 Solving -8 + x = 9.237604307 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 = 9.237604307 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.237604307 + 8 x = 9.237604307 + 8 Combine like terms: 9.237604307 + 8 = 17.237604307 x = 17.237604307 Simplifying x = 17.237604307Subproblem 2
x + -8 = -9.237604307 Simplifying x + -8 = -9.237604307 Reorder the terms: -8 + x = -9.237604307 Solving -8 + x = -9.237604307 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 = -9.237604307 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.237604307 + 8 x = -9.237604307 + 8 Combine like terms: -9.237604307 + 8 = -1.237604307 x = -1.237604307 Simplifying x = -1.237604307Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.237604307, -1.237604307}
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