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Simplifying 21x2 + 24x + -9 = 0 Reorder the terms: -9 + 24x + 21x2 = 0 Solving -9 + 24x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 8x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 8x + 7x2)' equal to zero and attempt to solve: Simplifying -3 + 8x + 7x2 = 0 Solving -3 + 8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 1.142857143x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 1.142857143x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 1.142857143x + x2 = 0 + 0.4285714286 1.142857143x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 1.142857143x + x2 = 0.4285714286 The x term is 1.142857143x. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143x + 0.3265306123 + x2 = 0.4285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 0.4285714286 + 0.3265306123 Combine like terms: 0.4285714286 + 0.3265306123 = 0.7551020409 0.3265306123 + 1.142857143x + x2 = 0.7551020409 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 0.7551020409 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 0.868966076 and -0.868966076.Subproblem 1
x + 0.5714285715 = 0.868966076 Simplifying x + 0.5714285715 = 0.868966076 Reorder the terms: 0.5714285715 + x = 0.868966076 Solving 0.5714285715 + x = 0.868966076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = 0.868966076 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 0.868966076 + -0.5714285715 x = 0.868966076 + -0.5714285715 Combine like terms: 0.868966076 + -0.5714285715 = 0.2975375045 x = 0.2975375045 Simplifying x = 0.2975375045Subproblem 2
x + 0.5714285715 = -0.868966076 Simplifying x + 0.5714285715 = -0.868966076 Reorder the terms: 0.5714285715 + x = -0.868966076 Solving 0.5714285715 + x = -0.868966076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = -0.868966076 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -0.868966076 + -0.5714285715 x = -0.868966076 + -0.5714285715 Combine like terms: -0.868966076 + -0.5714285715 = -1.4403946475 x = -1.4403946475 Simplifying x = -1.4403946475Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2975375045, -1.4403946475}Solution
x = {0.2975375045, -1.4403946475}
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