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Simplifying 4x2 + 14x + 1 = 0 Reorder the terms: 1 + 14x + 4x2 = 0 Solving 1 + 14x + 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'. 0.25 + 3.5x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.5x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.5x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.5x + x2 = 0 + -0.25 3.5x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.5x + x2 = -0.25 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -0.25 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -0.25 + 3.0625 Combine like terms: -0.25 + 3.0625 = 2.8125 3.0625 + 3.5x + x2 = 2.8125 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x + 1.75) equal to 1.677050983 and -1.677050983.Subproblem 1
x + 1.75 = 1.677050983 Simplifying x + 1.75 = 1.677050983 Reorder the terms: 1.75 + x = 1.677050983 Solving 1.75 + x = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.677050983 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.677050983 + -1.75 x = 1.677050983 + -1.75 Combine like terms: 1.677050983 + -1.75 = -0.072949017 x = -0.072949017 Simplifying x = -0.072949017Subproblem 2
x + 1.75 = -1.677050983 Simplifying x + 1.75 = -1.677050983 Reorder the terms: 1.75 + x = -1.677050983 Solving 1.75 + x = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.677050983 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.677050983 + -1.75 x = -1.677050983 + -1.75 Combine like terms: -1.677050983 + -1.75 = -3.427050983 x = -3.427050983 Simplifying x = -3.427050983Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.072949017, -3.427050983}
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