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Simplifying 63x2 + 73x + 21 = 0 Reorder the terms: 21 + 73x + 63x2 = 0 Solving 21 + 73x + 63x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. 0.3333333333 + 1.158730159x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 1.158730159x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 1.158730159x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 1.158730159x + x2 = 0 + -0.3333333333 1.158730159x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 1.158730159x + x2 = -0.3333333333 The x term is 1.158730159x. Take half its coefficient (0.5793650795). Square it (0.3356638953) and add it to both sides. Add '0.3356638953' to each side of the equation. 1.158730159x + 0.3356638953 + x2 = -0.3333333333 + 0.3356638953 Reorder the terms: 0.3356638953 + 1.158730159x + x2 = -0.3333333333 + 0.3356638953 Combine like terms: -0.3333333333 + 0.3356638953 = 0.002330562 0.3356638953 + 1.158730159x + x2 = 0.002330562 Factor a perfect square on the left side: (x + 0.5793650795)(x + 0.5793650795) = 0.002330562 Calculate the square root of the right side: 0.048275895 Break this problem into two subproblems by setting (x + 0.5793650795) equal to 0.048275895 and -0.048275895.Subproblem 1
x + 0.5793650795 = 0.048275895 Simplifying x + 0.5793650795 = 0.048275895 Reorder the terms: 0.5793650795 + x = 0.048275895 Solving 0.5793650795 + x = 0.048275895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5793650795' to each side of the equation. 0.5793650795 + -0.5793650795 + x = 0.048275895 + -0.5793650795 Combine like terms: 0.5793650795 + -0.5793650795 = 0.0000000000 0.0000000000 + x = 0.048275895 + -0.5793650795 x = 0.048275895 + -0.5793650795 Combine like terms: 0.048275895 + -0.5793650795 = -0.5310891845 x = -0.5310891845 Simplifying x = -0.5310891845Subproblem 2
x + 0.5793650795 = -0.048275895 Simplifying x + 0.5793650795 = -0.048275895 Reorder the terms: 0.5793650795 + x = -0.048275895 Solving 0.5793650795 + x = -0.048275895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5793650795' to each side of the equation. 0.5793650795 + -0.5793650795 + x = -0.048275895 + -0.5793650795 Combine like terms: 0.5793650795 + -0.5793650795 = 0.0000000000 0.0000000000 + x = -0.048275895 + -0.5793650795 x = -0.048275895 + -0.5793650795 Combine like terms: -0.048275895 + -0.5793650795 = -0.6276409745 x = -0.6276409745 Simplifying x = -0.6276409745Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5310891845, -0.6276409745}
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