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Simplifying 3x2 + -24x + -47 = 0 Reorder the terms: -47 + -24x + 3x2 = 0 Solving -47 + -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'. -15.66666667 + -8x + x2 = 0 Move the constant term to the right: Add '15.66666667' to each side of the equation. -15.66666667 + -8x + 15.66666667 + x2 = 0 + 15.66666667 Reorder the terms: -15.66666667 + 15.66666667 + -8x + x2 = 0 + 15.66666667 Combine like terms: -15.66666667 + 15.66666667 = 0.00000000 0.00000000 + -8x + x2 = 0 + 15.66666667 -8x + x2 = 0 + 15.66666667 Combine like terms: 0 + 15.66666667 = 15.66666667 -8x + x2 = 15.66666667 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 = 15.66666667 + 16 Reorder the terms: 16 + -8x + x2 = 15.66666667 + 16 Combine like terms: 15.66666667 + 16 = 31.66666667 16 + -8x + x2 = 31.66666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 31.66666667 Calculate the square root of the right side: 5.627314339 Break this problem into two subproblems by setting (x + -4) equal to 5.627314339 and -5.627314339.Subproblem 1
x + -4 = 5.627314339 Simplifying x + -4 = 5.627314339 Reorder the terms: -4 + x = 5.627314339 Solving -4 + x = 5.627314339 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 = 5.627314339 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.627314339 + 4 x = 5.627314339 + 4 Combine like terms: 5.627314339 + 4 = 9.627314339 x = 9.627314339 Simplifying x = 9.627314339Subproblem 2
x + -4 = -5.627314339 Simplifying x + -4 = -5.627314339 Reorder the terms: -4 + x = -5.627314339 Solving -4 + x = -5.627314339 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 = -5.627314339 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.627314339 + 4 x = -5.627314339 + 4 Combine like terms: -5.627314339 + 4 = -1.627314339 x = -1.627314339 Simplifying x = -1.627314339Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.627314339, -1.627314339}
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