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Simplifying 3x2 + 9x + -13 = 0 Reorder the terms: -13 + 9x + 3x2 = 0 Solving -13 + 9x + 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'. -4.333333333 + 3x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + 3x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + 3x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + 3x + x2 = 0 + 4.333333333 3x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 3x + x2 = 4.333333333 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 4.333333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 4.333333333 + 2.25 Combine like terms: 4.333333333 + 2.25 = 6.583333333 2.25 + 3x + x2 = 6.583333333 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 6.583333333 Calculate the square root of the right side: 2.56580072 Break this problem into two subproblems by setting (x + 1.5) equal to 2.56580072 and -2.56580072.Subproblem 1
x + 1.5 = 2.56580072 Simplifying x + 1.5 = 2.56580072 Reorder the terms: 1.5 + x = 2.56580072 Solving 1.5 + x = 2.56580072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.56580072 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.56580072 + -1.5 x = 2.56580072 + -1.5 Combine like terms: 2.56580072 + -1.5 = 1.06580072 x = 1.06580072 Simplifying x = 1.06580072Subproblem 2
x + 1.5 = -2.56580072 Simplifying x + 1.5 = -2.56580072 Reorder the terms: 1.5 + x = -2.56580072 Solving 1.5 + x = -2.56580072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.56580072 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.56580072 + -1.5 x = -2.56580072 + -1.5 Combine like terms: -2.56580072 + -1.5 = -4.06580072 x = -4.06580072 Simplifying x = -4.06580072Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.06580072, -4.06580072}
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