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Simplifying 3x2 + 9x = 22 Reorder the terms: 9x + 3x2 = 22 Solving 9x + 3x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 9x + 3x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.333333333 + 3x + x2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + 3x + 7.333333333 + x2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + 3x + x2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + 3x + x2 = 0 + 7.333333333 3x + x2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 3x + x2 = 7.333333333 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 = 7.333333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 7.333333333 + 2.25 Combine like terms: 7.333333333 + 2.25 = 9.583333333 2.25 + 3x + x2 = 9.583333333 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 9.583333333 Calculate the square root of the right side: 3.095695937 Break this problem into two subproblems by setting (x + 1.5) equal to 3.095695937 and -3.095695937.Subproblem 1
x + 1.5 = 3.095695937 Simplifying x + 1.5 = 3.095695937 Reorder the terms: 1.5 + x = 3.095695937 Solving 1.5 + x = 3.095695937 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 = 3.095695937 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.095695937 + -1.5 x = 3.095695937 + -1.5 Combine like terms: 3.095695937 + -1.5 = 1.595695937 x = 1.595695937 Simplifying x = 1.595695937Subproblem 2
x + 1.5 = -3.095695937 Simplifying x + 1.5 = -3.095695937 Reorder the terms: 1.5 + x = -3.095695937 Solving 1.5 + x = -3.095695937 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 = -3.095695937 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.095695937 + -1.5 x = -3.095695937 + -1.5 Combine like terms: -3.095695937 + -1.5 = -4.595695937 x = -4.595695937 Simplifying x = -4.595695937Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.595695937, -4.595695937}
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