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Simplifying 0.2x(x + -50) + 6 = 0.4(3x + 20) Reorder the terms: 0.2x(-50 + x) + 6 = 0.4(3x + 20) (-50 * 0.2x + x * 0.2x) + 6 = 0.4(3x + 20) (-10x + 0.2x2) + 6 = 0.4(3x + 20) Reorder the terms: 6 + -10x + 0.2x2 = 0.4(3x + 20) Reorder the terms: 6 + -10x + 0.2x2 = 0.4(20 + 3x) 6 + -10x + 0.2x2 = (20 * 0.4 + 3x * 0.4) 6 + -10x + 0.2x2 = (8 + 1.2x) Solving 6 + -10x + 0.2x2 = 8 + 1.2x Solving for variable 'x'. Reorder the terms: 6 + -8 + -10x + -1.2x + 0.2x2 = 8 + 1.2x + -8 + -1.2x Combine like terms: 6 + -8 = -2 -2 + -10x + -1.2x + 0.2x2 = 8 + 1.2x + -8 + -1.2x Combine like terms: -10x + -1.2x = -11.2x -2 + -11.2x + 0.2x2 = 8 + 1.2x + -8 + -1.2x Reorder the terms: -2 + -11.2x + 0.2x2 = 8 + -8 + 1.2x + -1.2x Combine like terms: 8 + -8 = 0 -2 + -11.2x + 0.2x2 = 0 + 1.2x + -1.2x -2 + -11.2x + 0.2x2 = 1.2x + -1.2x Combine like terms: 1.2x + -1.2x = 0.0 -2 + -11.2x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -10 + -56x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -56x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -56x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -56x + x2 = 0 + 10 -56x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -56x + x2 = 10 The x term is -56x. Take half its coefficient (-28). Square it (784) and add it to both sides. Add '784' to each side of the equation. -56x + 784 + x2 = 10 + 784 Reorder the terms: 784 + -56x + x2 = 10 + 784 Combine like terms: 10 + 784 = 794 784 + -56x + x2 = 794 Factor a perfect square on the left side: (x + -28)(x + -28) = 794 Calculate the square root of the right side: 28.178005607 Break this problem into two subproblems by setting (x + -28) equal to 28.178005607 and -28.178005607.Subproblem 1
x + -28 = 28.178005607 Simplifying x + -28 = 28.178005607 Reorder the terms: -28 + x = 28.178005607 Solving -28 + x = 28.178005607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 28.178005607 + 28 Combine like terms: -28 + 28 = 0 0 + x = 28.178005607 + 28 x = 28.178005607 + 28 Combine like terms: 28.178005607 + 28 = 56.178005607 x = 56.178005607 Simplifying x = 56.178005607Subproblem 2
x + -28 = -28.178005607 Simplifying x + -28 = -28.178005607 Reorder the terms: -28 + x = -28.178005607 Solving -28 + x = -28.178005607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = -28.178005607 + 28 Combine like terms: -28 + 28 = 0 0 + x = -28.178005607 + 28 x = -28.178005607 + 28 Combine like terms: -28.178005607 + 28 = -0.178005607 x = -0.178005607 Simplifying x = -0.178005607Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.178005607, -0.178005607}
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