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Simplifying -4.9x2 + 217x + 423 = 0 Reorder the terms: 423 + 217x + -4.9x2 = 0 Solving 423 + 217x + -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'. -86.32653061 + -44.28571429x + x2 = 0 Move the constant term to the right: Add '86.32653061' to each side of the equation. -86.32653061 + -44.28571429x + 86.32653061 + x2 = 0 + 86.32653061 Reorder the terms: -86.32653061 + 86.32653061 + -44.28571429x + x2 = 0 + 86.32653061 Combine like terms: -86.32653061 + 86.32653061 = 0.00000000 0.00000000 + -44.28571429x + x2 = 0 + 86.32653061 -44.28571429x + x2 = 0 + 86.32653061 Combine like terms: 0 + 86.32653061 = 86.32653061 -44.28571429x + x2 = 86.32653061 The x term is -44.28571429x. Take half its coefficient (-22.14285715). Square it (490.3061228) and add it to both sides. Add '490.3061228' to each side of the equation. -44.28571429x + 490.3061228 + x2 = 86.32653061 + 490.3061228 Reorder the terms: 490.3061228 + -44.28571429x + x2 = 86.32653061 + 490.3061228 Combine like terms: 86.32653061 + 490.3061228 = 576.63265341 490.3061228 + -44.28571429x + x2 = 576.63265341 Factor a perfect square on the left side: (x + -22.14285715)(x + -22.14285715) = 576.63265341 Calculate the square root of the right side: 24.013176662 Break this problem into two subproblems by setting (x + -22.14285715) equal to 24.013176662 and -24.013176662.Subproblem 1
x + -22.14285715 = 24.013176662 Simplifying x + -22.14285715 = 24.013176662 Reorder the terms: -22.14285715 + x = 24.013176662 Solving -22.14285715 + x = 24.013176662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.14285715' to each side of the equation. -22.14285715 + 22.14285715 + x = 24.013176662 + 22.14285715 Combine like terms: -22.14285715 + 22.14285715 = 0.00000000 0.00000000 + x = 24.013176662 + 22.14285715 x = 24.013176662 + 22.14285715 Combine like terms: 24.013176662 + 22.14285715 = 46.156033812 x = 46.156033812 Simplifying x = 46.156033812Subproblem 2
x + -22.14285715 = -24.013176662 Simplifying x + -22.14285715 = -24.013176662 Reorder the terms: -22.14285715 + x = -24.013176662 Solving -22.14285715 + x = -24.013176662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.14285715' to each side of the equation. -22.14285715 + 22.14285715 + x = -24.013176662 + 22.14285715 Combine like terms: -22.14285715 + 22.14285715 = 0.00000000 0.00000000 + x = -24.013176662 + 22.14285715 x = -24.013176662 + 22.14285715 Combine like terms: -24.013176662 + 22.14285715 = -1.870319512 x = -1.870319512 Simplifying x = -1.870319512Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.156033812, -1.870319512}
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