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Simplifying 3x2 + -9x = 13 Reorder the terms: -9x + 3x2 = 13 Solving -9x + 3x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -9x + 3x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -9x + 3x2 = 0 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 = 4.06580072 x = 4.06580072 Simplifying x = 4.06580072Subproblem 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 = -1.06580072 x = -1.06580072 Simplifying x = -1.06580072Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.06580072, -1.06580072}
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