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Simplifying (6x + -19)(3x + 10) = 180 Reorder the terms: (-19 + 6x)(3x + 10) = 180 Reorder the terms: (-19 + 6x)(10 + 3x) = 180 Multiply (-19 + 6x) * (10 + 3x) (-19(10 + 3x) + 6x * (10 + 3x)) = 180 ((10 * -19 + 3x * -19) + 6x * (10 + 3x)) = 180 ((-190 + -57x) + 6x * (10 + 3x)) = 180 (-190 + -57x + (10 * 6x + 3x * 6x)) = 180 (-190 + -57x + (60x + 18x2)) = 180 Combine like terms: -57x + 60x = 3x (-190 + 3x + 18x2) = 180 Solving -190 + 3x + 18x2 = 180 Solving for variable 'x'. Reorder the terms: -190 + -180 + 3x + 18x2 = 180 + -180 Combine like terms: -190 + -180 = -370 -370 + 3x + 18x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -370 + 3x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -20.55555556 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '20.55555556' to each side of the equation. -20.55555556 + 0.1666666667x + 20.55555556 + x2 = 0 + 20.55555556 Reorder the terms: -20.55555556 + 20.55555556 + 0.1666666667x + x2 = 0 + 20.55555556 Combine like terms: -20.55555556 + 20.55555556 = 0.00000000 0.00000000 + 0.1666666667x + x2 = 0 + 20.55555556 0.1666666667x + x2 = 0 + 20.55555556 Combine like terms: 0 + 20.55555556 = 20.55555556 0.1666666667x + x2 = 20.55555556 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 20.55555556 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 20.55555556 + 0.006944444447 Combine like terms: 20.55555556 + 0.006944444447 = 20.562500004447 0.006944444447 + 0.1666666667x + x2 = 20.562500004447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 20.562500004447 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 4.534589287 and -4.534589287.Subproblem 1
x + 0.08333333335 = 4.534589287 Simplifying x + 0.08333333335 = 4.534589287 Reorder the terms: 0.08333333335 + x = 4.534589287 Solving 0.08333333335 + x = 4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 4.534589287 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 4.534589287 + -0.08333333335 x = 4.534589287 + -0.08333333335 Combine like terms: 4.534589287 + -0.08333333335 = 4.45125595365 x = 4.45125595365 Simplifying x = 4.45125595365Subproblem 2
x + 0.08333333335 = -4.534589287 Simplifying x + 0.08333333335 = -4.534589287 Reorder the terms: 0.08333333335 + x = -4.534589287 Solving 0.08333333335 + x = -4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -4.534589287 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -4.534589287 + -0.08333333335 x = -4.534589287 + -0.08333333335 Combine like terms: -4.534589287 + -0.08333333335 = -4.61792262035 x = -4.61792262035 Simplifying x = -4.61792262035Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.45125595365, -4.61792262035}
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