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Simplifying (3x + -4)(x + -5) = 200 Reorder the terms: (-4 + 3x)(x + -5) = 200 Reorder the terms: (-4 + 3x)(-5 + x) = 200 Multiply (-4 + 3x) * (-5 + x) (-4(-5 + x) + 3x * (-5 + x)) = 200 ((-5 * -4 + x * -4) + 3x * (-5 + x)) = 200 ((20 + -4x) + 3x * (-5 + x)) = 200 (20 + -4x + (-5 * 3x + x * 3x)) = 200 (20 + -4x + (-15x + 3x2)) = 200 Combine like terms: -4x + -15x = -19x (20 + -19x + 3x2) = 200 Solving 20 + -19x + 3x2 = 200 Solving for variable 'x'. Reorder the terms: 20 + -200 + -19x + 3x2 = 200 + -200 Combine like terms: 20 + -200 = -180 -180 + -19x + 3x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -180 + -19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -6.333333333x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -6.333333333x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -6.333333333x + x2 = 0 + 60 -6.333333333x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -6.333333333x + x2 = 60 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = 60 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = 60 + 10.02777778 Combine like terms: 60 + 10.02777778 = 70.02777778 10.02777778 + -6.333333333x + x2 = 70.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 70.02777778 Calculate the square root of the right side: 8.368260141 Break this problem into two subproblems by setting (x + -3.166666667) equal to 8.368260141 and -8.368260141.Subproblem 1
x + -3.166666667 = 8.368260141 Simplifying x + -3.166666667 = 8.368260141 Reorder the terms: -3.166666667 + x = 8.368260141 Solving -3.166666667 + x = 8.368260141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 8.368260141 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 8.368260141 + 3.166666667 x = 8.368260141 + 3.166666667 Combine like terms: 8.368260141 + 3.166666667 = 11.534926808 x = 11.534926808 Simplifying x = 11.534926808Subproblem 2
x + -3.166666667 = -8.368260141 Simplifying x + -3.166666667 = -8.368260141 Reorder the terms: -3.166666667 + x = -8.368260141 Solving -3.166666667 + x = -8.368260141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -8.368260141 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -8.368260141 + 3.166666667 x = -8.368260141 + 3.166666667 Combine like terms: -8.368260141 + 3.166666667 = -5.201593474 x = -5.201593474 Simplifying x = -5.201593474Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.534926808, -5.201593474}
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