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Simplifying 2x(x + -5) = 3(x + 2) + 5 Reorder the terms: 2x(-5 + x) = 3(x + 2) + 5 (-5 * 2x + x * 2x) = 3(x + 2) + 5 (-10x + 2x2) = 3(x + 2) + 5 Reorder the terms: -10x + 2x2 = 3(2 + x) + 5 -10x + 2x2 = (2 * 3 + x * 3) + 5 -10x + 2x2 = (6 + 3x) + 5 Reorder the terms: -10x + 2x2 = 6 + 5 + 3x Combine like terms: 6 + 5 = 11 -10x + 2x2 = 11 + 3x Solving -10x + 2x2 = 11 + 3x Solving for variable 'x'. Reorder the terms: -11 + -10x + -3x + 2x2 = 11 + 3x + -11 + -3x Combine like terms: -10x + -3x = -13x -11 + -13x + 2x2 = 11 + 3x + -11 + -3x Reorder the terms: -11 + -13x + 2x2 = 11 + -11 + 3x + -3x Combine like terms: 11 + -11 = 0 -11 + -13x + 2x2 = 0 + 3x + -3x -11 + -13x + 2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -11 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -6.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -6.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -6.5x + x2 = 0 + 5.5 -6.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -6.5x + x2 = 5.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 5.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 5.5 + 10.5625 Combine like terms: 5.5 + 10.5625 = 16.0625 10.5625 + -6.5x + x2 = 16.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 16.0625 Calculate the square root of the right side: 4.007804885 Break this problem into two subproblems by setting (x + -3.25) equal to 4.007804885 and -4.007804885.Subproblem 1
x + -3.25 = 4.007804885 Simplifying x + -3.25 = 4.007804885 Reorder the terms: -3.25 + x = 4.007804885 Solving -3.25 + x = 4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.007804885 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.007804885 + 3.25 x = 4.007804885 + 3.25 Combine like terms: 4.007804885 + 3.25 = 7.257804885 x = 7.257804885 Simplifying x = 7.257804885Subproblem 2
x + -3.25 = -4.007804885 Simplifying x + -3.25 = -4.007804885 Reorder the terms: -3.25 + x = -4.007804885 Solving -3.25 + x = -4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.007804885 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.007804885 + 3.25 x = -4.007804885 + 3.25 Combine like terms: -4.007804885 + 3.25 = -0.757804885 x = -0.757804885 Simplifying x = -0.757804885Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.257804885, -0.757804885}
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