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Simplifying 4.9x2 + 70x + -3320 = 0 Reorder the terms: -3320 + 70x + 4.9x2 = 0 Solving -3320 + 70x + 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'. -677.5510204 + 14.28571429x + x2 = 0 Move the constant term to the right: Add '677.5510204' to each side of the equation. -677.5510204 + 14.28571429x + 677.5510204 + x2 = 0 + 677.5510204 Reorder the terms: -677.5510204 + 677.5510204 + 14.28571429x + x2 = 0 + 677.5510204 Combine like terms: -677.5510204 + 677.5510204 = 0.0000000 0.0000000 + 14.28571429x + x2 = 0 + 677.5510204 14.28571429x + x2 = 0 + 677.5510204 Combine like terms: 0 + 677.5510204 = 677.5510204 14.28571429x + x2 = 677.5510204 The x term is 14.28571429x. Take half its coefficient (7.142857145). Square it (51.02040819) and add it to both sides. Add '51.02040819' to each side of the equation. 14.28571429x + 51.02040819 + x2 = 677.5510204 + 51.02040819 Reorder the terms: 51.02040819 + 14.28571429x + x2 = 677.5510204 + 51.02040819 Combine like terms: 677.5510204 + 51.02040819 = 728.57142859 51.02040819 + 14.28571429x + x2 = 728.57142859 Factor a perfect square on the left side: (x + 7.142857145)(x + 7.142857145) = 728.57142859 Calculate the square root of the right side: 26.992062326 Break this problem into two subproblems by setting (x + 7.142857145) equal to 26.992062326 and -26.992062326.Subproblem 1
x + 7.142857145 = 26.992062326 Simplifying x + 7.142857145 = 26.992062326 Reorder the terms: 7.142857145 + x = 26.992062326 Solving 7.142857145 + x = 26.992062326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + x = 26.992062326 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = 26.992062326 + -7.142857145 x = 26.992062326 + -7.142857145 Combine like terms: 26.992062326 + -7.142857145 = 19.849205181 x = 19.849205181 Simplifying x = 19.849205181Subproblem 2
x + 7.142857145 = -26.992062326 Simplifying x + 7.142857145 = -26.992062326 Reorder the terms: 7.142857145 + x = -26.992062326 Solving 7.142857145 + x = -26.992062326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + x = -26.992062326 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = -26.992062326 + -7.142857145 x = -26.992062326 + -7.142857145 Combine like terms: -26.992062326 + -7.142857145 = -34.134919471 x = -34.134919471 Simplifying x = -34.134919471Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.849205181, -34.134919471}
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