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Simplifying 4x2 + 28x + 1 = 0 Reorder the terms: 1 + 28x + 4x2 = 0 Solving 1 + 28x + 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 + 7x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 7x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 7x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 7x + x2 = 0 + -0.25 7x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 7x + x2 = -0.25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -0.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -0.25 + 12.25 Combine like terms: -0.25 + 12.25 = 12 12.25 + 7x + x2 = 12 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 3.5) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 3.5 = 3.464101615 Simplifying x + 3.5 = 3.464101615 Reorder the terms: 3.5 + x = 3.464101615 Solving 3.5 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.464101615 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.464101615 + -3.5 x = 3.464101615 + -3.5 Combine like terms: 3.464101615 + -3.5 = -0.035898385 x = -0.035898385 Simplifying x = -0.035898385Subproblem 2
x + 3.5 = -3.464101615 Simplifying x + 3.5 = -3.464101615 Reorder the terms: 3.5 + x = -3.464101615 Solving 3.5 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.464101615 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.464101615 + -3.5 x = -3.464101615 + -3.5 Combine like terms: -3.464101615 + -3.5 = -6.964101615 x = -6.964101615 Simplifying x = -6.964101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.035898385, -6.964101615}
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