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Simplifying 5x2 + 10x + 4 = 0 Reorder the terms: 4 + 10x + 5x2 = 0 Solving 4 + 10x + 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'. 0.8 + 2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 2x + x2 = 0 + -0.8 2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 2x + x2 = -0.8 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.8 + 1 Reorder the terms: 1 + 2x + x2 = -0.8 + 1 Combine like terms: -0.8 + 1 = 0.2 1 + 2x + x2 = 0.2 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + 1) equal to 0.447213596 and -0.447213596.Subproblem 1
x + 1 = 0.447213596 Simplifying x + 1 = 0.447213596 Reorder the terms: 1 + x = 0.447213596 Solving 1 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.447213596 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.447213596 + -1 x = 0.447213596 + -1 Combine like terms: 0.447213596 + -1 = -0.552786404 x = -0.552786404 Simplifying x = -0.552786404Subproblem 2
x + 1 = -0.447213596 Simplifying x + 1 = -0.447213596 Reorder the terms: 1 + x = -0.447213596 Solving 1 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.447213596 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.447213596 + -1 x = -0.447213596 + -1 Combine like terms: -0.447213596 + -1 = -1.447213596 x = -1.447213596 Simplifying x = -1.447213596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.552786404, -1.447213596}
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