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Simplifying 5x2 + 35x + 36 = 0 Reorder the terms: 36 + 35x + 5x2 = 0 Solving 36 + 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'. 7.2 + 7x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + 7x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + 7x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + 7x + x2 = 0 + -7.2 7x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 7x + x2 = -7.2 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 = -7.2 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -7.2 + 12.25 Combine like terms: -7.2 + 12.25 = 5.05 12.25 + 7x + x2 = 5.05 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 5.05 Calculate the square root of the right side: 2.247220505 Break this problem into two subproblems by setting (x + 3.5) equal to 2.247220505 and -2.247220505.Subproblem 1
x + 3.5 = 2.247220505 Simplifying x + 3.5 = 2.247220505 Reorder the terms: 3.5 + x = 2.247220505 Solving 3.5 + x = 2.247220505 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 = 2.247220505 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.247220505 + -3.5 x = 2.247220505 + -3.5 Combine like terms: 2.247220505 + -3.5 = -1.252779495 x = -1.252779495 Simplifying x = -1.252779495Subproblem 2
x + 3.5 = -2.247220505 Simplifying x + 3.5 = -2.247220505 Reorder the terms: 3.5 + x = -2.247220505 Solving 3.5 + x = -2.247220505 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 = -2.247220505 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.247220505 + -3.5 x = -2.247220505 + -3.5 Combine like terms: -2.247220505 + -3.5 = -5.747220505 x = -5.747220505 Simplifying x = -5.747220505Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.252779495, -5.747220505}
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