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Simplifying 3x(x + 10) = 16 Reorder the terms: 3x(10 + x) = 16 (10 * 3x + x * 3x) = 16 (30x + 3x2) = 16 Solving 30x + 3x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 30x + 3x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + 10x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 10x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 10x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 10x + x2 = 0 + 5.333333333 10x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 10x + x2 = 5.333333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 5.333333333 + 25 Reorder the terms: 25 + 10x + x2 = 5.333333333 + 25 Combine like terms: 5.333333333 + 25 = 30.333333333 25 + 10x + x2 = 30.333333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 30.333333333 Calculate the square root of the right side: 5.507570547 Break this problem into two subproblems by setting (x + 5) equal to 5.507570547 and -5.507570547.Subproblem 1
x + 5 = 5.507570547 Simplifying x + 5 = 5.507570547 Reorder the terms: 5 + x = 5.507570547 Solving 5 + x = 5.507570547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.507570547 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.507570547 + -5 x = 5.507570547 + -5 Combine like terms: 5.507570547 + -5 = 0.507570547 x = 0.507570547 Simplifying x = 0.507570547Subproblem 2
x + 5 = -5.507570547 Simplifying x + 5 = -5.507570547 Reorder the terms: 5 + x = -5.507570547 Solving 5 + x = -5.507570547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.507570547 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.507570547 + -5 x = -5.507570547 + -5 Combine like terms: -5.507570547 + -5 = -10.507570547 x = -10.507570547 Simplifying x = -10.507570547Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.507570547, -10.507570547}
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