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Simplifying 2 + 24x = 3x2 + -15x Reorder the terms: 2 + 24x = -15x + 3x2 Solving 2 + 24x = -15x + 3x2 Solving for variable 'x'. Combine like terms: 24x + 15x = 39x 2 + 39x + -3x2 = -15x + 3x2 + 15x + -3x2 Reorder the terms: 2 + 39x + -3x2 = -15x + 15x + 3x2 + -3x2 Combine like terms: -15x + 15x = 0 2 + 39x + -3x2 = 0 + 3x2 + -3x2 2 + 39x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 2 + 39x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + -13x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -13x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -13x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -13x + x2 = 0 + 0.6666666667 -13x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -13x + x2 = 0.6666666667 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 0.6666666667 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 0.6666666667 + 42.25 Combine like terms: 0.6666666667 + 42.25 = 42.9166666667 42.25 + -13x + x2 = 42.9166666667 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 42.9166666667 Calculate the square root of the right side: 6.551081336 Break this problem into two subproblems by setting (x + -6.5) equal to 6.551081336 and -6.551081336.Subproblem 1
x + -6.5 = 6.551081336 Simplifying x + -6.5 = 6.551081336 Reorder the terms: -6.5 + x = 6.551081336 Solving -6.5 + x = 6.551081336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.551081336 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.551081336 + 6.5 x = 6.551081336 + 6.5 Combine like terms: 6.551081336 + 6.5 = 13.051081336 x = 13.051081336 Simplifying x = 13.051081336Subproblem 2
x + -6.5 = -6.551081336 Simplifying x + -6.5 = -6.551081336 Reorder the terms: -6.5 + x = -6.551081336 Solving -6.5 + x = -6.551081336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.551081336 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.551081336 + 6.5 x = -6.551081336 + 6.5 Combine like terms: -6.551081336 + 6.5 = -0.051081336 x = -0.051081336 Simplifying x = -0.051081336Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.051081336, -0.051081336}
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