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Simplifying 17(x + 2)(x + -5) = 18 Reorder the terms: 17(2 + x)(x + -5) = 18 Reorder the terms: 17(2 + x)(-5 + x) = 18 Multiply (2 + x) * (-5 + x) 17(2(-5 + x) + x(-5 + x)) = 18 17((-5 * 2 + x * 2) + x(-5 + x)) = 18 17((-10 + 2x) + x(-5 + x)) = 18 17(-10 + 2x + (-5 * x + x * x)) = 18 17(-10 + 2x + (-5x + x2)) = 18 Combine like terms: 2x + -5x = -3x 17(-10 + -3x + x2) = 18 (-10 * 17 + -3x * 17 + x2 * 17) = 18 (-170 + -51x + 17x2) = 18 Solving -170 + -51x + 17x2 = 18 Solving for variable 'x'. Reorder the terms: -170 + -18 + -51x + 17x2 = 18 + -18 Combine like terms: -170 + -18 = -188 -188 + -51x + 17x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -188 + -51x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -11.05882353 + -3x + x2 = 0 Move the constant term to the right: Add '11.05882353' to each side of the equation. -11.05882353 + -3x + 11.05882353 + x2 = 0 + 11.05882353 Reorder the terms: -11.05882353 + 11.05882353 + -3x + x2 = 0 + 11.05882353 Combine like terms: -11.05882353 + 11.05882353 = 0.00000000 0.00000000 + -3x + x2 = 0 + 11.05882353 -3x + x2 = 0 + 11.05882353 Combine like terms: 0 + 11.05882353 = 11.05882353 -3x + x2 = 11.05882353 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 11.05882353 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 11.05882353 + 2.25 Combine like terms: 11.05882353 + 2.25 = 13.30882353 2.25 + -3x + x2 = 13.30882353 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 13.30882353 Calculate the square root of the right side: 3.64812603 Break this problem into two subproblems by setting (x + -1.5) equal to 3.64812603 and -3.64812603.Subproblem 1
x + -1.5 = 3.64812603 Simplifying x + -1.5 = 3.64812603 Reorder the terms: -1.5 + x = 3.64812603 Solving -1.5 + x = 3.64812603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.64812603 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.64812603 + 1.5 x = 3.64812603 + 1.5 Combine like terms: 3.64812603 + 1.5 = 5.14812603 x = 5.14812603 Simplifying x = 5.14812603Subproblem 2
x + -1.5 = -3.64812603 Simplifying x + -1.5 = -3.64812603 Reorder the terms: -1.5 + x = -3.64812603 Solving -1.5 + x = -3.64812603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.64812603 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.64812603 + 1.5 x = -3.64812603 + 1.5 Combine like terms: -3.64812603 + 1.5 = -2.14812603 x = -2.14812603 Simplifying x = -2.14812603Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.14812603, -2.14812603}
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