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Simplifying (2x + -3)(x + -7) = 3 Reorder the terms: (-3 + 2x)(x + -7) = 3 Reorder the terms: (-3 + 2x)(-7 + x) = 3 Multiply (-3 + 2x) * (-7 + x) (-3(-7 + x) + 2x * (-7 + x)) = 3 ((-7 * -3 + x * -3) + 2x * (-7 + x)) = 3 ((21 + -3x) + 2x * (-7 + x)) = 3 (21 + -3x + (-7 * 2x + x * 2x)) = 3 (21 + -3x + (-14x + 2x2)) = 3 Combine like terms: -3x + -14x = -17x (21 + -17x + 2x2) = 3 Solving 21 + -17x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: 21 + -3 + -17x + 2x2 = 3 + -3 Combine like terms: 21 + -3 = 18 18 + -17x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 18 + -17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9 + -8.5x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8.5x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -8.5x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8.5x + x2 = 0 + -9 -8.5x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8.5x + x2 = -9 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -9 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -9 + 18.0625 Combine like terms: -9 + 18.0625 = 9.0625 18.0625 + -8.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -4.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -4.25 = 3.010398645 Simplifying x + -4.25 = 3.010398645 Reorder the terms: -4.25 + x = 3.010398645 Solving -4.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 3.010398645 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.010398645 + 4.25 x = 3.010398645 + 4.25 Combine like terms: 3.010398645 + 4.25 = 7.260398645 x = 7.260398645 Simplifying x = 7.260398645Subproblem 2
x + -4.25 = -3.010398645 Simplifying x + -4.25 = -3.010398645 Reorder the terms: -4.25 + x = -3.010398645 Solving -4.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -3.010398645 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.010398645 + 4.25 x = -3.010398645 + 4.25 Combine like terms: -3.010398645 + 4.25 = 1.239601355 x = 1.239601355 Simplifying x = 1.239601355Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.260398645, 1.239601355}
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