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Simplifying 3x(x + -5) = 6x2 + -16 Reorder the terms: 3x(-5 + x) = 6x2 + -16 (-5 * 3x + x * 3x) = 6x2 + -16 (-15x + 3x2) = 6x2 + -16 Reorder the terms: -15x + 3x2 = -16 + 6x2 Solving -15x + 3x2 = -16 + 6x2 Solving for variable 'x'. Reorder the terms: 16 + -15x + 3x2 + -6x2 = -16 + 6x2 + 16 + -6x2 Combine like terms: 3x2 + -6x2 = -3x2 16 + -15x + -3x2 = -16 + 6x2 + 16 + -6x2 Reorder the terms: 16 + -15x + -3x2 = -16 + 16 + 6x2 + -6x2 Combine like terms: -16 + 16 = 0 16 + -15x + -3x2 = 0 + 6x2 + -6x2 16 + -15x + -3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 16 + -15x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -5.333333333 + 5x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 5x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 5x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 5x + x2 = 0 + 5.333333333 5x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 5x + x2 = 5.333333333 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 5.333333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 5.333333333 + 6.25 Combine like terms: 5.333333333 + 6.25 = 11.583333333 6.25 + 5x + x2 = 11.583333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 11.583333333 Calculate the square root of the right side: 3.403429643 Break this problem into two subproblems by setting (x + 2.5) equal to 3.403429643 and -3.403429643.Subproblem 1
x + 2.5 = 3.403429643 Simplifying x + 2.5 = 3.403429643 Reorder the terms: 2.5 + x = 3.403429643 Solving 2.5 + x = 3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.403429643 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.403429643 + -2.5 x = 3.403429643 + -2.5 Combine like terms: 3.403429643 + -2.5 = 0.903429643 x = 0.903429643 Simplifying x = 0.903429643Subproblem 2
x + 2.5 = -3.403429643 Simplifying x + 2.5 = -3.403429643 Reorder the terms: 2.5 + x = -3.403429643 Solving 2.5 + x = -3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.403429643 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.403429643 + -2.5 x = -3.403429643 + -2.5 Combine like terms: -3.403429643 + -2.5 = -5.903429643 x = -5.903429643 Simplifying x = -5.903429643Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.903429643, -5.903429643}
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