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Simplifying 4.9x2 + 24x = 13 Reorder the terms: 24x + 4.9x2 = 13 Solving 24x + 4.9x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 24x + 4.9x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 24x + 4.9x2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.653061224 + 4.897959184x + x2 = 0 Move the constant term to the right: Add '2.653061224' to each side of the equation. -2.653061224 + 4.897959184x + 2.653061224 + x2 = 0 + 2.653061224 Reorder the terms: -2.653061224 + 2.653061224 + 4.897959184x + x2 = 0 + 2.653061224 Combine like terms: -2.653061224 + 2.653061224 = 0.000000000 0.000000000 + 4.897959184x + x2 = 0 + 2.653061224 4.897959184x + x2 = 0 + 2.653061224 Combine like terms: 0 + 2.653061224 = 2.653061224 4.897959184x + x2 = 2.653061224 The x term is 4.897959184x. Take half its coefficient (2.448979592). Square it (5.997501042) and add it to both sides. Add '5.997501042' to each side of the equation. 4.897959184x + 5.997501042 + x2 = 2.653061224 + 5.997501042 Reorder the terms: 5.997501042 + 4.897959184x + x2 = 2.653061224 + 5.997501042 Combine like terms: 2.653061224 + 5.997501042 = 8.650562266 5.997501042 + 4.897959184x + x2 = 8.650562266 Factor a perfect square on the left side: (x + 2.448979592)(x + 2.448979592) = 8.650562266 Calculate the square root of the right side: 2.941183821 Break this problem into two subproblems by setting (x + 2.448979592) equal to 2.941183821 and -2.941183821.Subproblem 1
x + 2.448979592 = 2.941183821 Simplifying x + 2.448979592 = 2.941183821 Reorder the terms: 2.448979592 + x = 2.941183821 Solving 2.448979592 + x = 2.941183821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.448979592' to each side of the equation. 2.448979592 + -2.448979592 + x = 2.941183821 + -2.448979592 Combine like terms: 2.448979592 + -2.448979592 = 0.000000000 0.000000000 + x = 2.941183821 + -2.448979592 x = 2.941183821 + -2.448979592 Combine like terms: 2.941183821 + -2.448979592 = 0.492204229 x = 0.492204229 Simplifying x = 0.492204229Subproblem 2
x + 2.448979592 = -2.941183821 Simplifying x + 2.448979592 = -2.941183821 Reorder the terms: 2.448979592 + x = -2.941183821 Solving 2.448979592 + x = -2.941183821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.448979592' to each side of the equation. 2.448979592 + -2.448979592 + x = -2.941183821 + -2.448979592 Combine like terms: 2.448979592 + -2.448979592 = 0.000000000 0.000000000 + x = -2.941183821 + -2.448979592 x = -2.941183821 + -2.448979592 Combine like terms: -2.941183821 + -2.448979592 = -5.390163413 x = -5.390163413 Simplifying x = -5.390163413Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.492204229, -5.390163413}
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