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Simplifying 5x2 + 66x + 3 = 0 Reorder the terms: 3 + 66x + 5x2 = 0 Solving 3 + 66x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 13.2x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 13.2x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 13.2x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 13.2x + x2 = 0 + -0.6 13.2x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 13.2x + x2 = -0.6 The x term is 13.2x. Take half its coefficient (6.6). Square it (43.56) and add it to both sides. Add '43.56' to each side of the equation. 13.2x + 43.56 + x2 = -0.6 + 43.56 Reorder the terms: 43.56 + 13.2x + x2 = -0.6 + 43.56 Combine like terms: -0.6 + 43.56 = 42.96 43.56 + 13.2x + x2 = 42.96 Factor a perfect square on the left side: (x + 6.6)(x + 6.6) = 42.96 Calculate the square root of the right side: 6.554387843 Break this problem into two subproblems by setting (x + 6.6) equal to 6.554387843 and -6.554387843.Subproblem 1
x + 6.6 = 6.554387843 Simplifying x + 6.6 = 6.554387843 Reorder the terms: 6.6 + x = 6.554387843 Solving 6.6 + x = 6.554387843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = 6.554387843 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = 6.554387843 + -6.6 x = 6.554387843 + -6.6 Combine like terms: 6.554387843 + -6.6 = -0.045612157 x = -0.045612157 Simplifying x = -0.045612157Subproblem 2
x + 6.6 = -6.554387843 Simplifying x + 6.6 = -6.554387843 Reorder the terms: 6.6 + x = -6.554387843 Solving 6.6 + x = -6.554387843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = -6.554387843 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = -6.554387843 + -6.6 x = -6.554387843 + -6.6 Combine like terms: -6.554387843 + -6.6 = -13.154387843 x = -13.154387843 Simplifying x = -13.154387843Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.045612157, -13.154387843}
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