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Simplifying 0.6612 + 4x + 4x2 = 0 Solving 0.6612 + 4x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.1653 + x + x2 = 0 Move the constant term to the right: Add '-0.1653' to each side of the equation. 0.1653 + x + -0.1653 + x2 = 0 + -0.1653 Reorder the terms: 0.1653 + -0.1653 + x + x2 = 0 + -0.1653 Combine like terms: 0.1653 + -0.1653 = 0.0000 0.0000 + x + x2 = 0 + -0.1653 x + x2 = 0 + -0.1653 Combine like terms: 0 + -0.1653 = -0.1653 x + x2 = -0.1653 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. + 0.25 + x2 = -0.1653 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.1653 + 0.25 Combine like terms: -0.1653 + 0.25 = 0.0847 1.25 + x2 = 0.0847 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.0847 Calculate the square root of the right side: 0.291032644 Break this problem into two subproblems by setting (x + 0.5) equal to 0.291032644 and -0.291032644.Subproblem 1
x + 0.5 = 0.291032644 Simplifying x + 0.5 = 0.291032644 Reorder the terms: 0.5 + x = 0.291032644 Solving 0.5 + x = 0.291032644 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 = 0.291032644 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.291032644 + -0.5 x = 0.291032644 + -0.5 Combine like terms: 0.291032644 + -0.5 = -0.208967356 x = -0.208967356 Simplifying x = -0.208967356Subproblem 2
x + 0.5 = -0.291032644 Simplifying x + 0.5 = -0.291032644 Reorder the terms: 0.5 + x = -0.291032644 Solving 0.5 + x = -0.291032644 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 = -0.291032644 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.291032644 + -0.5 x = -0.291032644 + -0.5 Combine like terms: -0.291032644 + -0.5 = -0.791032644 x = -0.791032644 Simplifying x = -0.791032644Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.208967356, -0.791032644}
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