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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 = 0.33333333 16 + 8x + x2 = 0.33333333 Factor a perfect square on the left side: (x + 4)(x + 4) = 0.33333333 Calculate the square root of the right side: 0.577350266 Break this problem into two subproblems by setting (x + 4) equal to 0.577350266 and -0.577350266.Subproblem 1
x + 4 = 0.577350266 Simplifying x + 4 = 0.577350266 Reorder the terms: 4 + x = 0.577350266 Solving 4 + x = 0.577350266 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 = 0.577350266 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0.577350266 + -4 x = 0.577350266 + -4 Combine like terms: 0.577350266 + -4 = -3.422649734 x = -3.422649734 Simplifying x = -3.422649734Subproblem 2
x + 4 = -0.577350266 Simplifying x + 4 = -0.577350266 Reorder the terms: 4 + x = -0.577350266 Solving 4 + x = -0.577350266 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 = -0.577350266 + -4 Combine like terms: 4 + -4 = 0 0 + x = -0.577350266 + -4 x = -0.577350266 + -4 Combine like terms: -0.577350266 + -4 = -4.577350266 x = -4.577350266 Simplifying x = -4.577350266Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.422649734, -4.577350266}
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