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Simplifying 0 = -4.9x2 + 18.9x + 2.8 Reorder the terms: 0 = 2.8 + 18.9x + -4.9x2 Solving 0 = 2.8 + 18.9x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -2.8 = -2.8 -2.8 + -18.9x + 4.9x2 = 2.8 + 18.9x + -4.9x2 + -2.8 + -18.9x + 4.9x2 Reorder the terms: -2.8 + -18.9x + 4.9x2 = 2.8 + -2.8 + 18.9x + -18.9x + -4.9x2 + 4.9x2 Combine like terms: 2.8 + -2.8 = 0.0 -2.8 + -18.9x + 4.9x2 = 0.0 + 18.9x + -18.9x + -4.9x2 + 4.9x2 -2.8 + -18.9x + 4.9x2 = 18.9x + -18.9x + -4.9x2 + 4.9x2 Combine like terms: 18.9x + -18.9x = 0.0 -2.8 + -18.9x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -2.8 + -18.9x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -2.8 + -18.9x + 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'. -0.5714285714 + -3.857142857x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -3.857142857x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -3.857142857x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -3.857142857x + x2 = 0 + 0.5714285714 -3.857142857x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -3.857142857x + x2 = 0.5714285714 The x term is -3.857142857x. Take half its coefficient (-1.928571429). Square it (3.719387757) and add it to both sides. Add '3.719387757' to each side of the equation. -3.857142857x + 3.719387757 + x2 = 0.5714285714 + 3.719387757 Reorder the terms: 3.719387757 + -3.857142857x + x2 = 0.5714285714 + 3.719387757 Combine like terms: 0.5714285714 + 3.719387757 = 4.2908163284 3.719387757 + -3.857142857x + x2 = 4.2908163284 Factor a perfect square on the left side: (x + -1.928571429)(x + -1.928571429) = 4.2908163284 Calculate the square root of the right side: 2.071428572 Break this problem into two subproblems by setting (x + -1.928571429) equal to 2.071428572 and -2.071428572.Subproblem 1
x + -1.928571429 = 2.071428572 Simplifying x + -1.928571429 = 2.071428572 Reorder the terms: -1.928571429 + x = 2.071428572 Solving -1.928571429 + x = 2.071428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.928571429' to each side of the equation. -1.928571429 + 1.928571429 + x = 2.071428572 + 1.928571429 Combine like terms: -1.928571429 + 1.928571429 = 0.000000000 0.000000000 + x = 2.071428572 + 1.928571429 x = 2.071428572 + 1.928571429 Combine like terms: 2.071428572 + 1.928571429 = 4.000000001 x = 4.000000001 Simplifying x = 4.000000001Subproblem 2
x + -1.928571429 = -2.071428572 Simplifying x + -1.928571429 = -2.071428572 Reorder the terms: -1.928571429 + x = -2.071428572 Solving -1.928571429 + x = -2.071428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.928571429' to each side of the equation. -1.928571429 + 1.928571429 + x = -2.071428572 + 1.928571429 Combine like terms: -1.928571429 + 1.928571429 = 0.000000000 0.000000000 + x = -2.071428572 + 1.928571429 x = -2.071428572 + 1.928571429 Combine like terms: -2.071428572 + 1.928571429 = -0.142857143 x = -0.142857143 Simplifying x = -0.142857143Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.000000001, -0.142857143}
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