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Simplifying 3(x + -5) * 2x = 5x + -15 Reorder the terms: 3(-5 + x) * 2x = 5x + -15 Reorder the terms for easier multiplication: 3 * 2x(-5 + x) = 5x + -15 Multiply 3 * 2 6x(-5 + x) = 5x + -15 (-5 * 6x + x * 6x) = 5x + -15 (-30x + 6x2) = 5x + -15 Reorder the terms: -30x + 6x2 = -15 + 5x Solving -30x + 6x2 = -15 + 5x Solving for variable 'x'. Reorder the terms: 15 + -30x + -5x + 6x2 = -15 + 5x + 15 + -5x Combine like terms: -30x + -5x = -35x 15 + -35x + 6x2 = -15 + 5x + 15 + -5x Reorder the terms: 15 + -35x + 6x2 = -15 + 15 + 5x + -5x Combine like terms: -15 + 15 = 0 15 + -35x + 6x2 = 0 + 5x + -5x 15 + -35x + 6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 15 + -35x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + -5.833333333x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5.833333333x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5.833333333x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5.833333333x + x2 = 0 + -2.5 -5.833333333x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5.833333333x + x2 = -2.5 The x term is -5.833333333x. Take half its coefficient (-2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. -5.833333333x + 8.506944446 + x2 = -2.5 + 8.506944446 Reorder the terms: 8.506944446 + -5.833333333x + x2 = -2.5 + 8.506944446 Combine like terms: -2.5 + 8.506944446 = 6.006944446 8.506944446 + -5.833333333x + x2 = 6.006944446 Factor a perfect square on the left side: (x + -2.916666667)(x + -2.916666667) = 6.006944446 Calculate the square root of the right side: 2.450906862 Break this problem into two subproblems by setting (x + -2.916666667) equal to 2.450906862 and -2.450906862.Subproblem 1
x + -2.916666667 = 2.450906862 Simplifying x + -2.916666667 = 2.450906862 Reorder the terms: -2.916666667 + x = 2.450906862 Solving -2.916666667 + x = 2.450906862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = 2.450906862 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = 2.450906862 + 2.916666667 x = 2.450906862 + 2.916666667 Combine like terms: 2.450906862 + 2.916666667 = 5.367573529 x = 5.367573529 Simplifying x = 5.367573529Subproblem 2
x + -2.916666667 = -2.450906862 Simplifying x + -2.916666667 = -2.450906862 Reorder the terms: -2.916666667 + x = -2.450906862 Solving -2.916666667 + x = -2.450906862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = -2.450906862 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = -2.450906862 + 2.916666667 x = -2.450906862 + 2.916666667 Combine like terms: -2.450906862 + 2.916666667 = 0.465759805 x = 0.465759805 Simplifying x = 0.465759805Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.367573529, 0.465759805}
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