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Simplifying 3x * x + x = 100 Multiply x * x 3x2 + x = 100 Reorder the terms: x + 3x2 = 100 Solving x + 3x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + x + 3x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -33.33333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + 0.3333333333x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + 0.3333333333x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 33.33333333 0.3333333333x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 0.3333333333x + x2 = 33.33333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 33.33333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 33.33333333 + 0.25 Combine like terms: 33.33333333 + 0.25 = 33.58333333 0.25 + 0.3333333333x + x2 = 33.58333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 33.58333333 Calculate the square root of the right side: 5.795112883 Break this problem into two subproblems by setting (x + 0.5) equal to 5.795112883 and -5.795112883.Subproblem 1
x + 0.5 = 5.795112883 Simplifying x + 0.5 = 5.795112883 Reorder the terms: 0.5 + x = 5.795112883 Solving 0.5 + x = 5.795112883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.795112883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.795112883 + -0.5 x = 5.795112883 + -0.5 Combine like terms: 5.795112883 + -0.5 = 5.295112883 x = 5.295112883 Simplifying x = 5.295112883Subproblem 2
x + 0.5 = -5.795112883 Simplifying x + 0.5 = -5.795112883 Reorder the terms: 0.5 + x = -5.795112883 Solving 0.5 + x = -5.795112883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.795112883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.795112883 + -0.5 x = -5.795112883 + -0.5 Combine like terms: -5.795112883 + -0.5 = -6.295112883 x = -6.295112883 Simplifying x = -6.295112883Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.295112883, -6.295112883}
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