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Simplifying 3.5x2 + 35x + 9 = 0 Reorder the terms: 9 + 35x + 3.5x2 = 0 Solving 9 + 35x + 3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. 2.571428571 + 10x + x2 = 0 Move the constant term to the right: Add '-2.571428571' to each side of the equation. 2.571428571 + 10x + -2.571428571 + x2 = 0 + -2.571428571 Reorder the terms: 2.571428571 + -2.571428571 + 10x + x2 = 0 + -2.571428571 Combine like terms: 2.571428571 + -2.571428571 = 0.000000000 0.000000000 + 10x + x2 = 0 + -2.571428571 10x + x2 = 0 + -2.571428571 Combine like terms: 0 + -2.571428571 = -2.571428571 10x + x2 = -2.571428571 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -2.571428571 + 25 Reorder the terms: 25 + 10x + x2 = -2.571428571 + 25 Combine like terms: -2.571428571 + 25 = 22.428571429 25 + 10x + x2 = 22.428571429 Factor a perfect square on the left side: (x + 5)(x + 5) = 22.428571429 Calculate the square root of the right side: 4.735881273 Break this problem into two subproblems by setting (x + 5) equal to 4.735881273 and -4.735881273.Subproblem 1
x + 5 = 4.735881273 Simplifying x + 5 = 4.735881273 Reorder the terms: 5 + x = 4.735881273 Solving 5 + x = 4.735881273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.735881273 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.735881273 + -5 x = 4.735881273 + -5 Combine like terms: 4.735881273 + -5 = -0.264118727 x = -0.264118727 Simplifying x = -0.264118727Subproblem 2
x + 5 = -4.735881273 Simplifying x + 5 = -4.735881273 Reorder the terms: 5 + x = -4.735881273 Solving 5 + x = -4.735881273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.735881273 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.735881273 + -5 x = -4.735881273 + -5 Combine like terms: -4.735881273 + -5 = -9.735881273 x = -9.735881273 Simplifying x = -9.735881273Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.264118727, -9.735881273}
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