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Simplifying 24 = -4.9x2 + 19.6x + 58.8 Reorder the terms: 24 = 58.8 + 19.6x + -4.9x2 Solving 24 = 58.8 + 19.6x + -4.9x2 Solving for variable 'x'. Combine like terms: 24 + -58.8 = -34.8 -34.8 + -19.6x + 4.9x2 = 58.8 + 19.6x + -4.9x2 + -58.8 + -19.6x + 4.9x2 Reorder the terms: -34.8 + -19.6x + 4.9x2 = 58.8 + -58.8 + 19.6x + -19.6x + -4.9x2 + 4.9x2 Combine like terms: 58.8 + -58.8 = 0.0 -34.8 + -19.6x + 4.9x2 = 0.0 + 19.6x + -19.6x + -4.9x2 + 4.9x2 -34.8 + -19.6x + 4.9x2 = 19.6x + -19.6x + -4.9x2 + 4.9x2 Combine like terms: 19.6x + -19.6x = 0.0 -34.8 + -19.6x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -34.8 + -19.6x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -34.8 + -19.6x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -7.102040816 + -4x + x2 = 0 Move the constant term to the right: Add '7.102040816' to each side of the equation. -7.102040816 + -4x + 7.102040816 + x2 = 0 + 7.102040816 Reorder the terms: -7.102040816 + 7.102040816 + -4x + x2 = 0 + 7.102040816 Combine like terms: -7.102040816 + 7.102040816 = 0.000000000 0.000000000 + -4x + x2 = 0 + 7.102040816 -4x + x2 = 0 + 7.102040816 Combine like terms: 0 + 7.102040816 = 7.102040816 -4x + x2 = 7.102040816 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 7.102040816 + 4 Reorder the terms: 4 + -4x + x2 = 7.102040816 + 4 Combine like terms: 7.102040816 + 4 = 11.102040816 4 + -4x + x2 = 11.102040816 Factor a perfect square on the left side: (x + -2)(x + -2) = 11.102040816 Calculate the square root of the right side: 3.331972511 Break this problem into two subproblems by setting (x + -2) equal to 3.331972511 and -3.331972511.Subproblem 1
x + -2 = 3.331972511 Simplifying x + -2 = 3.331972511 Reorder the terms: -2 + x = 3.331972511 Solving -2 + x = 3.331972511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.331972511 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.331972511 + 2 x = 3.331972511 + 2 Combine like terms: 3.331972511 + 2 = 5.331972511 x = 5.331972511 Simplifying x = 5.331972511Subproblem 2
x + -2 = -3.331972511 Simplifying x + -2 = -3.331972511 Reorder the terms: -2 + x = -3.331972511 Solving -2 + x = -3.331972511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.331972511 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.331972511 + 2 x = -3.331972511 + 2 Combine like terms: -3.331972511 + 2 = -1.331972511 x = -1.331972511 Simplifying x = -1.331972511Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.331972511, -1.331972511}
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