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Simplifying 5x2 + 35x + 12 = 0 Reorder the terms: 12 + 35x + 5x2 = 0 Solving 12 + 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'. 2.4 + 7x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 7x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 7x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 7x + x2 = 0 + -2.4 7x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 7x + x2 = -2.4 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 = -2.4 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -2.4 + 12.25 Combine like terms: -2.4 + 12.25 = 9.85 12.25 + 7x + x2 = 9.85 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 9.85 Calculate the square root of the right side: 3.138470965 Break this problem into two subproblems by setting (x + 3.5) equal to 3.138470965 and -3.138470965.Subproblem 1
x + 3.5 = 3.138470965 Simplifying x + 3.5 = 3.138470965 Reorder the terms: 3.5 + x = 3.138470965 Solving 3.5 + x = 3.138470965 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 = 3.138470965 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.138470965 + -3.5 x = 3.138470965 + -3.5 Combine like terms: 3.138470965 + -3.5 = -0.361529035 x = -0.361529035 Simplifying x = -0.361529035Subproblem 2
x + 3.5 = -3.138470965 Simplifying x + 3.5 = -3.138470965 Reorder the terms: 3.5 + x = -3.138470965 Solving 3.5 + x = -3.138470965 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 = -3.138470965 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.138470965 + -3.5 x = -3.138470965 + -3.5 Combine like terms: -3.138470965 + -3.5 = -6.638470965 x = -6.638470965 Simplifying x = -6.638470965Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.361529035, -6.638470965}
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