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Simplifying 3x2 + 6x + -25 = 0 Reorder the terms: -25 + 6x + 3x2 = 0 Solving -25 + 6x + 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'. -8.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + 2x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + 2x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + 8.333333333 2x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 2x + x2 = 8.333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 8.333333333 + 1 Reorder the terms: 1 + 2x + x2 = 8.333333333 + 1 Combine like terms: 8.333333333 + 1 = 9.333333333 1 + 2x + x2 = 9.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 9.333333333 Calculate the square root of the right side: 3.055050463 Break this problem into two subproblems by setting (x + 1) equal to 3.055050463 and -3.055050463.Subproblem 1
x + 1 = 3.055050463 Simplifying x + 1 = 3.055050463 Reorder the terms: 1 + x = 3.055050463 Solving 1 + x = 3.055050463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.055050463 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.055050463 + -1 x = 3.055050463 + -1 Combine like terms: 3.055050463 + -1 = 2.055050463 x = 2.055050463 Simplifying x = 2.055050463Subproblem 2
x + 1 = -3.055050463 Simplifying x + 1 = -3.055050463 Reorder the terms: 1 + x = -3.055050463 Solving 1 + x = -3.055050463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.055050463 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.055050463 + -1 x = -3.055050463 + -1 Combine like terms: -3.055050463 + -1 = -4.055050463 x = -4.055050463 Simplifying x = -4.055050463Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.055050463, -4.055050463}
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