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Simplifying -4.9x2 + 23.8x + 3.5 = 0 Reorder the terms: 3.5 + 23.8x + -4.9x2 = 0 Solving 3.5 + 23.8x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.7142857143 + -4.857142857x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -4.857142857x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -4.857142857x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -4.857142857x + x2 = 0 + 0.7142857143 -4.857142857x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -4.857142857x + x2 = 0.7142857143 The x term is -4.857142857x. Take half its coefficient (-2.428571429). Square it (5.897959186) and add it to both sides. Add '5.897959186' to each side of the equation. -4.857142857x + 5.897959186 + x2 = 0.7142857143 + 5.897959186 Reorder the terms: 5.897959186 + -4.857142857x + x2 = 0.7142857143 + 5.897959186 Combine like terms: 0.7142857143 + 5.897959186 = 6.6122449003 5.897959186 + -4.857142857x + x2 = 6.6122449003 Factor a perfect square on the left side: (x + -2.428571429)(x + -2.428571429) = 6.6122449003 Calculate the square root of the right side: 2.571428572 Break this problem into two subproblems by setting (x + -2.428571429) equal to 2.571428572 and -2.571428572.Subproblem 1
x + -2.428571429 = 2.571428572 Simplifying x + -2.428571429 = 2.571428572 Reorder the terms: -2.428571429 + x = 2.571428572 Solving -2.428571429 + x = 2.571428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.428571429' to each side of the equation. -2.428571429 + 2.428571429 + x = 2.571428572 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x = 2.571428572 + 2.428571429 x = 2.571428572 + 2.428571429 Combine like terms: 2.571428572 + 2.428571429 = 5.000000001 x = 5.000000001 Simplifying x = 5.000000001Subproblem 2
x + -2.428571429 = -2.571428572 Simplifying x + -2.428571429 = -2.571428572 Reorder the terms: -2.428571429 + x = -2.571428572 Solving -2.428571429 + x = -2.571428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.428571429' to each side of the equation. -2.428571429 + 2.428571429 + x = -2.571428572 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x = -2.571428572 + 2.428571429 x = -2.571428572 + 2.428571429 Combine like terms: -2.571428572 + 2.428571429 = -0.142857143 x = -0.142857143 Simplifying x = -0.142857143Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.000000001, -0.142857143}
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