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Simplifying 5x2 + 35x = 1 Reorder the terms: 35x + 5x2 = 1 Solving 35x + 5x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 35x + 5x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 35x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 7x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 7x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 7x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 7x + x2 = 0 + 0.2 7x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 7x + x2 = 0.2 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 = 0.2 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 0.2 + 12.25 Combine like terms: 0.2 + 12.25 = 12.45 12.25 + 7x + x2 = 12.45 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 12.45 Calculate the square root of the right side: 3.528455753 Break this problem into two subproblems by setting (x + 3.5) equal to 3.528455753 and -3.528455753.Subproblem 1
x + 3.5 = 3.528455753 Simplifying x + 3.5 = 3.528455753 Reorder the terms: 3.5 + x = 3.528455753 Solving 3.5 + x = 3.528455753 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 = 3.528455753 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.528455753 + -3.5 x = 3.528455753 + -3.5 Combine like terms: 3.528455753 + -3.5 = 0.028455753 x = 0.028455753 Simplifying x = 0.028455753Subproblem 2
x + 3.5 = -3.528455753 Simplifying x + 3.5 = -3.528455753 Reorder the terms: 3.5 + x = -3.528455753 Solving 3.5 + x = -3.528455753 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 = -3.528455753 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.528455753 + -3.5 x = -3.528455753 + -3.5 Combine like terms: -3.528455753 + -3.5 = -7.028455753 x = -7.028455753 Simplifying x = -7.028455753Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.028455753, -7.028455753}
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