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Simplifying 3x2 + 6x + -154 = 0 Reorder the terms: -154 + 6x + 3x2 = 0 Solving -154 + 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'. -51.33333333 + 2x + x2 = 0 Move the constant term to the right: Add '51.33333333' to each side of the equation. -51.33333333 + 2x + 51.33333333 + x2 = 0 + 51.33333333 Reorder the terms: -51.33333333 + 51.33333333 + 2x + x2 = 0 + 51.33333333 Combine like terms: -51.33333333 + 51.33333333 = 0.00000000 0.00000000 + 2x + x2 = 0 + 51.33333333 2x + x2 = 0 + 51.33333333 Combine like terms: 0 + 51.33333333 = 51.33333333 2x + x2 = 51.33333333 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 = 51.33333333 + 1 Reorder the terms: 1 + 2x + x2 = 51.33333333 + 1 Combine like terms: 51.33333333 + 1 = 52.33333333 1 + 2x + x2 = 52.33333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 52.33333333 Calculate the square root of the right side: 7.234178138 Break this problem into two subproblems by setting (x + 1) equal to 7.234178138 and -7.234178138.Subproblem 1
x + 1 = 7.234178138 Simplifying x + 1 = 7.234178138 Reorder the terms: 1 + x = 7.234178138 Solving 1 + x = 7.234178138 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 = 7.234178138 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.234178138 + -1 x = 7.234178138 + -1 Combine like terms: 7.234178138 + -1 = 6.234178138 x = 6.234178138 Simplifying x = 6.234178138Subproblem 2
x + 1 = -7.234178138 Simplifying x + 1 = -7.234178138 Reorder the terms: 1 + x = -7.234178138 Solving 1 + x = -7.234178138 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 = -7.234178138 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.234178138 + -1 x = -7.234178138 + -1 Combine like terms: -7.234178138 + -1 = -8.234178138 x = -8.234178138 Simplifying x = -8.234178138Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.234178138, -8.234178138}
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