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Simplifying 21x2 + 120x + 104 = 0 Reorder the terms: 104 + 120x + 21x2 = 0 Solving 104 + 120x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 4.952380952 + 5.714285714x + x2 = 0 Move the constant term to the right: Add '-4.952380952' to each side of the equation. 4.952380952 + 5.714285714x + -4.952380952 + x2 = 0 + -4.952380952 Reorder the terms: 4.952380952 + -4.952380952 + 5.714285714x + x2 = 0 + -4.952380952 Combine like terms: 4.952380952 + -4.952380952 = 0.000000000 0.000000000 + 5.714285714x + x2 = 0 + -4.952380952 5.714285714x + x2 = 0 + -4.952380952 Combine like terms: 0 + -4.952380952 = -4.952380952 5.714285714x + x2 = -4.952380952 The x term is 5.714285714x. Take half its coefficient (2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. 5.714285714x + 8.163265305 + x2 = -4.952380952 + 8.163265305 Reorder the terms: 8.163265305 + 5.714285714x + x2 = -4.952380952 + 8.163265305 Combine like terms: -4.952380952 + 8.163265305 = 3.210884353 8.163265305 + 5.714285714x + x2 = 3.210884353 Factor a perfect square on the left side: (x + 2.857142857)(x + 2.857142857) = 3.210884353 Calculate the square root of the right side: 1.791894069 Break this problem into two subproblems by setting (x + 2.857142857) equal to 1.791894069 and -1.791894069.Subproblem 1
x + 2.857142857 = 1.791894069 Simplifying x + 2.857142857 = 1.791894069 Reorder the terms: 2.857142857 + x = 1.791894069 Solving 2.857142857 + x = 1.791894069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = 1.791894069 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = 1.791894069 + -2.857142857 x = 1.791894069 + -2.857142857 Combine like terms: 1.791894069 + -2.857142857 = -1.065248788 x = -1.065248788 Simplifying x = -1.065248788Subproblem 2
x + 2.857142857 = -1.791894069 Simplifying x + 2.857142857 = -1.791894069 Reorder the terms: 2.857142857 + x = -1.791894069 Solving 2.857142857 + x = -1.791894069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = -1.791894069 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = -1.791894069 + -2.857142857 x = -1.791894069 + -2.857142857 Combine like terms: -1.791894069 + -2.857142857 = -4.649036926 x = -4.649036926 Simplifying x = -4.649036926Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.065248788, -4.649036926}
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