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Simplifying 3x2 + 30x + 10 = 0 Reorder the terms: 10 + 30x + 3x2 = 0 Solving 10 + 30x + 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'. 3.333333333 + 10x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 10x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 10x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 10x + x2 = 0 + -3.333333333 10x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 10x + x2 = -3.333333333 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 = -3.333333333 + 25 Reorder the terms: 25 + 10x + x2 = -3.333333333 + 25 Combine like terms: -3.333333333 + 25 = 21.666666667 25 + 10x + x2 = 21.666666667 Factor a perfect square on the left side: (x + 5)(x + 5) = 21.666666667 Calculate the square root of the right side: 4.654746681 Break this problem into two subproblems by setting (x + 5) equal to 4.654746681 and -4.654746681.Subproblem 1
x + 5 = 4.654746681 Simplifying x + 5 = 4.654746681 Reorder the terms: 5 + x = 4.654746681 Solving 5 + x = 4.654746681 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 = 4.654746681 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.654746681 + -5 x = 4.654746681 + -5 Combine like terms: 4.654746681 + -5 = -0.345253319 x = -0.345253319 Simplifying x = -0.345253319Subproblem 2
x + 5 = -4.654746681 Simplifying x + 5 = -4.654746681 Reorder the terms: 5 + x = -4.654746681 Solving 5 + x = -4.654746681 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 = -4.654746681 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.654746681 + -5 x = -4.654746681 + -5 Combine like terms: -4.654746681 + -5 = -9.654746681 x = -9.654746681 Simplifying x = -9.654746681Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.345253319, -9.654746681}
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