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Simplifying (5x2 + 35x + 27) = 0 Reorder the terms: (27 + 35x + 5x2) = 0 Remove parenthesis around (27 + 35x + 5x2) 27 + 35x + 5x2 = 0 Solving 27 + 35x + 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'. 5.4 + 7x + x2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + 7x + -5.4 + x2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + 7x + x2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + 7x + x2 = 0 + -5.4 7x + x2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 7x + x2 = -5.4 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 = -5.4 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -5.4 + 12.25 Combine like terms: -5.4 + 12.25 = 6.85 12.25 + 7x + x2 = 6.85 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 6.85 Calculate the square root of the right side: 2.617250466 Break this problem into two subproblems by setting (x + 3.5) equal to 2.617250466 and -2.617250466.Subproblem 1
x + 3.5 = 2.617250466 Simplifying x + 3.5 = 2.617250466 Reorder the terms: 3.5 + x = 2.617250466 Solving 3.5 + x = 2.617250466 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 = 2.617250466 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.617250466 + -3.5 x = 2.617250466 + -3.5 Combine like terms: 2.617250466 + -3.5 = -0.882749534 x = -0.882749534 Simplifying x = -0.882749534Subproblem 2
x + 3.5 = -2.617250466 Simplifying x + 3.5 = -2.617250466 Reorder the terms: 3.5 + x = -2.617250466 Solving 3.5 + x = -2.617250466 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 = -2.617250466 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.617250466 + -3.5 x = -2.617250466 + -3.5 Combine like terms: -2.617250466 + -3.5 = -6.117250466 x = -6.117250466 Simplifying x = -6.117250466Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.882749534, -6.117250466}
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