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Simplifying 48 = -4.9x2 + 52x + 30 Reorder the terms: 48 = 30 + 52x + -4.9x2 Solving 48 = 30 + 52x + -4.9x2 Solving for variable 'x'. Combine like terms: 48 + -30 = 18 18 + -52x + 4.9x2 = 30 + 52x + -4.9x2 + -30 + -52x + 4.9x2 Reorder the terms: 18 + -52x + 4.9x2 = 30 + -30 + 52x + -52x + -4.9x2 + 4.9x2 Combine like terms: 30 + -30 = 0 18 + -52x + 4.9x2 = 0 + 52x + -52x + -4.9x2 + 4.9x2 18 + -52x + 4.9x2 = 52x + -52x + -4.9x2 + 4.9x2 Combine like terms: 52x + -52x = 0 18 + -52x + 4.9x2 = 0 + -4.9x2 + 4.9x2 18 + -52x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 18 + -52x + 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'. 3.673469388 + -10.6122449x + x2 = 0 Move the constant term to the right: Add '-3.673469388' to each side of the equation. 3.673469388 + -10.6122449x + -3.673469388 + x2 = 0 + -3.673469388 Reorder the terms: 3.673469388 + -3.673469388 + -10.6122449x + x2 = 0 + -3.673469388 Combine like terms: 3.673469388 + -3.673469388 = 0.000000000 0.000000000 + -10.6122449x + x2 = 0 + -3.673469388 -10.6122449x + x2 = 0 + -3.673469388 Combine like terms: 0 + -3.673469388 = -3.673469388 -10.6122449x + x2 = -3.673469388 The x term is -10.6122449x. Take half its coefficient (-5.30612245). Square it (28.15493545) and add it to both sides. Add '28.15493545' to each side of the equation. -10.6122449x + 28.15493545 + x2 = -3.673469388 + 28.15493545 Reorder the terms: 28.15493545 + -10.6122449x + x2 = -3.673469388 + 28.15493545 Combine like terms: -3.673469388 + 28.15493545 = 24.481466062 28.15493545 + -10.6122449x + x2 = 24.481466062 Factor a perfect square on the left side: (x + -5.30612245)(x + -5.30612245) = 24.481466062 Calculate the square root of the right side: 4.947874904 Break this problem into two subproblems by setting (x + -5.30612245) equal to 4.947874904 and -4.947874904.Subproblem 1
x + -5.30612245 = 4.947874904 Simplifying x + -5.30612245 = 4.947874904 Reorder the terms: -5.30612245 + x = 4.947874904 Solving -5.30612245 + x = 4.947874904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.30612245' to each side of the equation. -5.30612245 + 5.30612245 + x = 4.947874904 + 5.30612245 Combine like terms: -5.30612245 + 5.30612245 = 0.00000000 0.00000000 + x = 4.947874904 + 5.30612245 x = 4.947874904 + 5.30612245 Combine like terms: 4.947874904 + 5.30612245 = 10.253997354 x = 10.253997354 Simplifying x = 10.253997354Subproblem 2
x + -5.30612245 = -4.947874904 Simplifying x + -5.30612245 = -4.947874904 Reorder the terms: -5.30612245 + x = -4.947874904 Solving -5.30612245 + x = -4.947874904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.30612245' to each side of the equation. -5.30612245 + 5.30612245 + x = -4.947874904 + 5.30612245 Combine like terms: -5.30612245 + 5.30612245 = 0.00000000 0.00000000 + x = -4.947874904 + 5.30612245 x = -4.947874904 + 5.30612245 Combine like terms: -4.947874904 + 5.30612245 = 0.358247546 x = 0.358247546 Simplifying x = 0.358247546Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.253997354, 0.358247546}
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