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Simplifying 21x2 + 3x + -12 = 0 Reorder the terms: -12 + 3x + 21x2 = 0 Solving -12 + 3x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + x + 7x2)' equal to zero and attempt to solve: Simplifying -4 + x + 7x2 = 0 Solving -4 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.1428571429x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.1428571429x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + 0.5714285714 0.1428571429x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.1428571429x + x2 = 0.5714285714 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1428571429x + 0.25 + x2 = 0.5714285714 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = 0.5714285714 + 0.25 Combine like terms: 0.5714285714 + 0.25 = 0.8214285714 0.25 + 0.1428571429x + x2 = 0.8214285714 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.8214285714 Calculate the square root of the right side: 0.906326967 Break this problem into two subproblems by setting (x + 0.5) equal to 0.906326967 and -0.906326967.Subproblem 1
x + 0.5 = 0.906326967 Simplifying x + 0.5 = 0.906326967 Reorder the terms: 0.5 + x = 0.906326967 Solving 0.5 + x = 0.906326967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.906326967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.906326967 + -0.5 x = 0.906326967 + -0.5 Combine like terms: 0.906326967 + -0.5 = 0.406326967 x = 0.406326967 Simplifying x = 0.406326967Subproblem 2
x + 0.5 = -0.906326967 Simplifying x + 0.5 = -0.906326967 Reorder the terms: 0.5 + x = -0.906326967 Solving 0.5 + x = -0.906326967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.906326967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.906326967 + -0.5 x = -0.906326967 + -0.5 Combine like terms: -0.906326967 + -0.5 = -1.406326967 x = -1.406326967 Simplifying x = -1.406326967Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.406326967, -1.406326967}Solution
x = {0.406326967, -1.406326967}
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