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Simplifying 3x2 + -24x + 5 = 0 Reorder the terms: 5 + -24x + 3x2 = 0 Solving 5 + -24x + 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'. 1.666666667 + -8x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -8x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -8x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -8x + x2 = 0 + -1.666666667 -8x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -8x + x2 = -1.666666667 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 = -1.666666667 + 16 Reorder the terms: 16 + -8x + x2 = -1.666666667 + 16 Combine like terms: -1.666666667 + 16 = 14.333333333 16 + -8x + x2 = 14.333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 14.333333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (x + -4) equal to 3.785938897 and -3.785938897.Subproblem 1
x + -4 = 3.785938897 Simplifying x + -4 = 3.785938897 Reorder the terms: -4 + x = 3.785938897 Solving -4 + x = 3.785938897 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 = 3.785938897 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.785938897 + 4 x = 3.785938897 + 4 Combine like terms: 3.785938897 + 4 = 7.785938897 x = 7.785938897 Simplifying x = 7.785938897Subproblem 2
x + -4 = -3.785938897 Simplifying x + -4 = -3.785938897 Reorder the terms: -4 + x = -3.785938897 Solving -4 + x = -3.785938897 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 = -3.785938897 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.785938897 + 4 x = -3.785938897 + 4 Combine like terms: -3.785938897 + 4 = 0.214061103 x = 0.214061103 Simplifying x = 0.214061103Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.785938897, 0.214061103}
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