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Simplifying 0.2x(x + 50) + -6 = 1.2x + 8 Reorder the terms: 0.2x(50 + x) + -6 = 1.2x + 8 (50 * 0.2x + x * 0.2x) + -6 = 1.2x + 8 (10x + 0.2x2) + -6 = 1.2x + 8 Reorder the terms: -6 + 10x + 0.2x2 = 1.2x + 8 Reorder the terms: -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 = -14 -14 + 10x + -1.2x + 0.2x2 = 8 + 1.2x + -8 + -1.2x Combine like terms: 10x + -1.2x = 8.8x -14 + 8.8x + 0.2x2 = 8 + 1.2x + -8 + -1.2x Reorder the terms: -14 + 8.8x + 0.2x2 = 8 + -8 + 1.2x + -1.2x Combine like terms: 8 + -8 = 0 -14 + 8.8x + 0.2x2 = 0 + 1.2x + -1.2x -14 + 8.8x + 0.2x2 = 1.2x + -1.2x Combine like terms: 1.2x + -1.2x = 0.0 -14 + 8.8x + 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'. -70 + 44x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 44x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 44x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 44x + x2 = 0 + 70 44x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 44x + x2 = 70 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = 70 + 484 Reorder the terms: 484 + 44x + x2 = 70 + 484 Combine like terms: 70 + 484 = 554 484 + 44x + x2 = 554 Factor a perfect square on the left side: (x + 22)(x + 22) = 554 Calculate the square root of the right side: 23.537204592 Break this problem into two subproblems by setting (x + 22) equal to 23.537204592 and -23.537204592.Subproblem 1
x + 22 = 23.537204592 Simplifying x + 22 = 23.537204592 Reorder the terms: 22 + x = 23.537204592 Solving 22 + x = 23.537204592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 23.537204592 + -22 Combine like terms: 22 + -22 = 0 0 + x = 23.537204592 + -22 x = 23.537204592 + -22 Combine like terms: 23.537204592 + -22 = 1.537204592 x = 1.537204592 Simplifying x = 1.537204592Subproblem 2
x + 22 = -23.537204592 Simplifying x + 22 = -23.537204592 Reorder the terms: 22 + x = -23.537204592 Solving 22 + x = -23.537204592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -23.537204592 + -22 Combine like terms: 22 + -22 = 0 0 + x = -23.537204592 + -22 x = -23.537204592 + -22 Combine like terms: -23.537204592 + -22 = -45.537204592 x = -45.537204592 Simplifying x = -45.537204592Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.537204592, -45.537204592}
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