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Simplifying -3(x + 2) + -1 = 2(x + -5) * 5x Reorder the terms: -3(2 + x) + -1 = 2(x + -5) * 5x (2 * -3 + x * -3) + -1 = 2(x + -5) * 5x (-6 + -3x) + -1 = 2(x + -5) * 5x Reorder the terms: -6 + -1 + -3x = 2(x + -5) * 5x Combine like terms: -6 + -1 = -7 -7 + -3x = 2(x + -5) * 5x Reorder the terms: -7 + -3x = 2(-5 + x) * 5x Reorder the terms for easier multiplication: -7 + -3x = 2 * 5x(-5 + x) Multiply 2 * 5 -7 + -3x = 10x(-5 + x) -7 + -3x = (-5 * 10x + x * 10x) -7 + -3x = (-50x + 10x2) Solving -7 + -3x = -50x + 10x2 Solving for variable 'x'. Combine like terms: -3x + 50x = 47x -7 + 47x + -10x2 = -50x + 10x2 + 50x + -10x2 Reorder the terms: -7 + 47x + -10x2 = -50x + 50x + 10x2 + -10x2 Combine like terms: -50x + 50x = 0 -7 + 47x + -10x2 = 0 + 10x2 + -10x2 -7 + 47x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -7 + 47x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 0.7 + -4.7x + x2 = 0 Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + -4.7x + -0.7 + x2 = 0 + -0.7 Reorder the terms: 0.7 + -0.7 + -4.7x + x2 = 0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + -4.7x + x2 = 0 + -0.7 -4.7x + x2 = 0 + -0.7 Combine like terms: 0 + -0.7 = -0.7 -4.7x + x2 = -0.7 The x term is -4.7x. Take half its coefficient (-2.35). Square it (5.5225) and add it to both sides. Add '5.5225' to each side of the equation. -4.7x + 5.5225 + x2 = -0.7 + 5.5225 Reorder the terms: 5.5225 + -4.7x + x2 = -0.7 + 5.5225 Combine like terms: -0.7 + 5.5225 = 4.8225 5.5225 + -4.7x + x2 = 4.8225 Factor a perfect square on the left side: (x + -2.35)(x + -2.35) = 4.8225 Calculate the square root of the right side: 2.196019126 Break this problem into two subproblems by setting (x + -2.35) equal to 2.196019126 and -2.196019126.Subproblem 1
x + -2.35 = 2.196019126 Simplifying x + -2.35 = 2.196019126 Reorder the terms: -2.35 + x = 2.196019126 Solving -2.35 + x = 2.196019126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.35' to each side of the equation. -2.35 + 2.35 + x = 2.196019126 + 2.35 Combine like terms: -2.35 + 2.35 = 0.00 0.00 + x = 2.196019126 + 2.35 x = 2.196019126 + 2.35 Combine like terms: 2.196019126 + 2.35 = 4.546019126 x = 4.546019126 Simplifying x = 4.546019126Subproblem 2
x + -2.35 = -2.196019126 Simplifying x + -2.35 = -2.196019126 Reorder the terms: -2.35 + x = -2.196019126 Solving -2.35 + x = -2.196019126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.35' to each side of the equation. -2.35 + 2.35 + x = -2.196019126 + 2.35 Combine like terms: -2.35 + 2.35 = 0.00 0.00 + x = -2.196019126 + 2.35 x = -2.196019126 + 2.35 Combine like terms: -2.196019126 + 2.35 = 0.153980874 x = 0.153980874 Simplifying x = 0.153980874Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.546019126, 0.153980874}
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