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Simplifying 6x + 3x2 + 24x = -5 Reorder the terms: 6x + 24x + 3x2 = -5 Combine like terms: 6x + 24x = 30x 30x + 3x2 = -5 Solving 30x + 3x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + 30x + 3x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 10x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 10x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 10x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 10x + x2 = 0 + -1.666666667 10x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 10x + x2 = -1.666666667 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -1.666666667 + 25 Reorder the terms: 25 + 10x + x2 = -1.666666667 + 25 Combine like terms: -1.666666667 + 25 = 23.333333333 25 + 10x + x2 = 23.333333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 23.333333333 Calculate the square root of the right side: 4.830458915 Break this problem into two subproblems by setting (x + 5) equal to 4.830458915 and -4.830458915.Subproblem 1
x + 5 = 4.830458915 Simplifying x + 5 = 4.830458915 Reorder the terms: 5 + x = 4.830458915 Solving 5 + x = 4.830458915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.830458915 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.830458915 + -5 x = 4.830458915 + -5 Combine like terms: 4.830458915 + -5 = -0.169541085 x = -0.169541085 Simplifying x = -0.169541085Subproblem 2
x + 5 = -4.830458915 Simplifying x + 5 = -4.830458915 Reorder the terms: 5 + x = -4.830458915 Solving 5 + x = -4.830458915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.830458915 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.830458915 + -5 x = -4.830458915 + -5 Combine like terms: -4.830458915 + -5 = -9.830458915 x = -9.830458915 Simplifying x = -9.830458915Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.169541085, -9.830458915}
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