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Simplifying 5x2 + 14x + 4 = 0 Reorder the terms: 4 + 14x + 5x2 = 0 Solving 4 + 14x + 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 + 2.8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 2.8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 2.8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 2.8x + x2 = 0 + -0.8 2.8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 2.8x + x2 = -0.8 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = -0.8 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -0.8 + 1.96 Combine like terms: -0.8 + 1.96 = 1.16 1.96 + 2.8x + x2 = 1.16 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (x + 1.4) equal to 1.077032961 and -1.077032961.Subproblem 1
x + 1.4 = 1.077032961 Simplifying x + 1.4 = 1.077032961 Reorder the terms: 1.4 + x = 1.077032961 Solving 1.4 + x = 1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 1.077032961 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 1.077032961 + -1.4 x = 1.077032961 + -1.4 Combine like terms: 1.077032961 + -1.4 = -0.322967039 x = -0.322967039 Simplifying x = -0.322967039Subproblem 2
x + 1.4 = -1.077032961 Simplifying x + 1.4 = -1.077032961 Reorder the terms: 1.4 + x = -1.077032961 Solving 1.4 + x = -1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -1.077032961 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -1.077032961 + -1.4 x = -1.077032961 + -1.4 Combine like terms: -1.077032961 + -1.4 = -2.477032961 x = -2.477032961 Simplifying x = -2.477032961Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.322967039, -2.477032961}
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