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Simplifying 3x2 + 342x + 10 = 0 Reorder the terms: 10 + 342x + 3x2 = 0 Solving 10 + 342x + 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 + 114x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 114x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 114x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 114x + x2 = 0 + -3.333333333 114x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 114x + x2 = -3.333333333 The x term is 114x. Take half its coefficient (57). Square it (3249) and add it to both sides. Add '3249' to each side of the equation. 114x + 3249 + x2 = -3.333333333 + 3249 Reorder the terms: 3249 + 114x + x2 = -3.333333333 + 3249 Combine like terms: -3.333333333 + 3249 = 3245.666666667 3249 + 114x + x2 = 3245.666666667 Factor a perfect square on the left side: (x + 57)(x + 57) = 3245.666666667 Calculate the square root of the right side: 56.97075273 Break this problem into two subproblems by setting (x + 57) equal to 56.97075273 and -56.97075273.Subproblem 1
x + 57 = 56.97075273 Simplifying x + 57 = 56.97075273 Reorder the terms: 57 + x = 56.97075273 Solving 57 + x = 56.97075273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-57' to each side of the equation. 57 + -57 + x = 56.97075273 + -57 Combine like terms: 57 + -57 = 0 0 + x = 56.97075273 + -57 x = 56.97075273 + -57 Combine like terms: 56.97075273 + -57 = -0.02924727 x = -0.02924727 Simplifying x = -0.02924727Subproblem 2
x + 57 = -56.97075273 Simplifying x + 57 = -56.97075273 Reorder the terms: 57 + x = -56.97075273 Solving 57 + x = -56.97075273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-57' to each side of the equation. 57 + -57 + x = -56.97075273 + -57 Combine like terms: 57 + -57 = 0 0 + x = -56.97075273 + -57 x = -56.97075273 + -57 Combine like terms: -56.97075273 + -57 = -113.97075273 x = -113.97075273 Simplifying x = -113.97075273Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.02924727, -113.97075273}
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