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Simplifying 18 = (2x + -3)(x + -1) Reorder the terms: 18 = (-3 + 2x)(x + -1) Reorder the terms: 18 = (-3 + 2x)(-1 + x) Multiply (-3 + 2x) * (-1 + x) 18 = (-3(-1 + x) + 2x * (-1 + x)) 18 = ((-1 * -3 + x * -3) + 2x * (-1 + x)) 18 = ((3 + -3x) + 2x * (-1 + x)) 18 = (3 + -3x + (-1 * 2x + x * 2x)) 18 = (3 + -3x + (-2x + 2x2)) Combine like terms: -3x + -2x = -5x 18 = (3 + -5x + 2x2) Solving 18 = 3 + -5x + 2x2 Solving for variable 'x'. Combine like terms: 18 + -3 = 15 15 + 5x + -2x2 = 3 + -5x + 2x2 + -3 + 5x + -2x2 Reorder the terms: 15 + 5x + -2x2 = 3 + -3 + -5x + 5x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 15 + 5x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2 15 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 15 + 5x + -2x2 = 0 + 2x2 + -2x2 15 + 5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 15 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -2.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -2.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -2.5x + x2 = 0 + 7.5 -2.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -2.5x + x2 = 7.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 7.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 7.5 + 1.5625 Combine like terms: 7.5 + 1.5625 = 9.0625 1.5625 + -2.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -1.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -1.25 = 3.010398645 Simplifying x + -1.25 = 3.010398645 Reorder the terms: -1.25 + x = 3.010398645 Solving -1.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.010398645 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.010398645 + 1.25 x = 3.010398645 + 1.25 Combine like terms: 3.010398645 + 1.25 = 4.260398645 x = 4.260398645 Simplifying x = 4.260398645Subproblem 2
x + -1.25 = -3.010398645 Simplifying x + -1.25 = -3.010398645 Reorder the terms: -1.25 + x = -3.010398645 Solving -1.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.010398645 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.010398645 + 1.25 x = -3.010398645 + 1.25 Combine like terms: -3.010398645 + 1.25 = -1.760398645 x = -1.760398645 Simplifying x = -1.760398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.260398645, -1.760398645}
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