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Simplifying 5x2 + 24x + -35 = 0 Reorder the terms: -35 + 24x + 5x2 = 0 Solving -35 + 24x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + 4.8x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 4.8x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 4.8x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4.8x + x2 = 0 + 7 4.8x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 4.8x + x2 = 7 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = 7 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 7 + 5.76 Combine like terms: 7 + 5.76 = 12.76 5.76 + 4.8x + x2 = 12.76 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 12.76 Calculate the square root of the right side: 3.57211422 Break this problem into two subproblems by setting (x + 2.4) equal to 3.57211422 and -3.57211422.Subproblem 1
x + 2.4 = 3.57211422 Simplifying x + 2.4 = 3.57211422 Reorder the terms: 2.4 + x = 3.57211422 Solving 2.4 + x = 3.57211422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 3.57211422 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 3.57211422 + -2.4 x = 3.57211422 + -2.4 Combine like terms: 3.57211422 + -2.4 = 1.17211422 x = 1.17211422 Simplifying x = 1.17211422Subproblem 2
x + 2.4 = -3.57211422 Simplifying x + 2.4 = -3.57211422 Reorder the terms: 2.4 + x = -3.57211422 Solving 2.4 + x = -3.57211422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -3.57211422 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -3.57211422 + -2.4 x = -3.57211422 + -2.4 Combine like terms: -3.57211422 + -2.4 = -5.97211422 x = -5.97211422 Simplifying x = -5.97211422Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.17211422, -5.97211422}
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