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Simplifying 3x2 + -48x + 140 = 0 Reorder the terms: 140 + -48x + 3x2 = 0 Solving 140 + -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'. 46.66666667 + -16x + x2 = 0 Move the constant term to the right: Add '-46.66666667' to each side of the equation. 46.66666667 + -16x + -46.66666667 + x2 = 0 + -46.66666667 Reorder the terms: 46.66666667 + -46.66666667 + -16x + x2 = 0 + -46.66666667 Combine like terms: 46.66666667 + -46.66666667 = 0.00000000 0.00000000 + -16x + x2 = 0 + -46.66666667 -16x + x2 = 0 + -46.66666667 Combine like terms: 0 + -46.66666667 = -46.66666667 -16x + x2 = -46.66666667 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 = -46.66666667 + 64 Reorder the terms: 64 + -16x + x2 = -46.66666667 + 64 Combine like terms: -46.66666667 + 64 = 17.33333333 64 + -16x + x2 = 17.33333333 Factor a perfect square on the left side: (x + -8)(x + -8) = 17.33333333 Calculate the square root of the right side: 4.163331999 Break this problem into two subproblems by setting (x + -8) equal to 4.163331999 and -4.163331999.Subproblem 1
x + -8 = 4.163331999 Simplifying x + -8 = 4.163331999 Reorder the terms: -8 + x = 4.163331999 Solving -8 + x = 4.163331999 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 = 4.163331999 + 8 Combine like terms: -8 + 8 = 0 0 + x = 4.163331999 + 8 x = 4.163331999 + 8 Combine like terms: 4.163331999 + 8 = 12.163331999 x = 12.163331999 Simplifying x = 12.163331999Subproblem 2
x + -8 = -4.163331999 Simplifying x + -8 = -4.163331999 Reorder the terms: -8 + x = -4.163331999 Solving -8 + x = -4.163331999 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 = -4.163331999 + 8 Combine like terms: -8 + 8 = 0 0 + x = -4.163331999 + 8 x = -4.163331999 + 8 Combine like terms: -4.163331999 + 8 = 3.836668001 x = 3.836668001 Simplifying x = 3.836668001Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.163331999, 3.836668001}
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