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Simplifying x + (2x + 3) + -2x(x + -5) = 6 Reorder the terms: x + (3 + 2x) + -2x(x + -5) = 6 Remove parenthesis around (3 + 2x) x + 3 + 2x + -2x(x + -5) = 6 Reorder the terms: x + 3 + 2x + -2x(-5 + x) = 6 x + 3 + 2x + (-5 * -2x + x * -2x) = 6 x + 3 + 2x + (10x + -2x2) = 6 Reorder the terms: 3 + x + 2x + 10x + -2x2 = 6 Combine like terms: x + 2x = 3x 3 + 3x + 10x + -2x2 = 6 Combine like terms: 3x + 10x = 13x 3 + 13x + -2x2 = 6 Solving 3 + 13x + -2x2 = 6 Solving for variable 'x'. Reorder the terms: 3 + -6 + 13x + -2x2 = 6 + -6 Combine like terms: 3 + -6 = -3 -3 + 13x + -2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -3 + 13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -6.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -6.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -6.5x + x2 = 0 + -1.5 -6.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -6.5x + x2 = -1.5 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 = -1.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -1.5 + 10.5625 Combine like terms: -1.5 + 10.5625 = 9.0625 10.5625 + -6.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -3.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -3.25 = 3.010398645 Simplifying x + -3.25 = 3.010398645 Reorder the terms: -3.25 + x = 3.010398645 Solving -3.25 + x = 3.010398645 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 = 3.010398645 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.010398645 + 3.25 x = 3.010398645 + 3.25 Combine like terms: 3.010398645 + 3.25 = 6.260398645 x = 6.260398645 Simplifying x = 6.260398645Subproblem 2
x + -3.25 = -3.010398645 Simplifying x + -3.25 = -3.010398645 Reorder the terms: -3.25 + x = -3.010398645 Solving -3.25 + x = -3.010398645 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 = -3.010398645 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.010398645 + 3.25 x = -3.010398645 + 3.25 Combine like terms: -3.010398645 + 3.25 = 0.239601355 x = 0.239601355 Simplifying x = 0.239601355Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.260398645, 0.239601355}
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