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Simplifying 2x2 + 30x + 25 = 0 Reorder the terms: 25 + 30x + 2x2 = 0 Solving 25 + 30x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + 15x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 15x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 15x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 15x + x2 = 0 + -12.5 15x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 15x + x2 = -12.5 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -12.5 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -12.5 + 56.25 Combine like terms: -12.5 + 56.25 = 43.75 56.25 + 15x + x2 = 43.75 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 43.75 Calculate the square root of the right side: 6.614378278 Break this problem into two subproblems by setting (x + 7.5) equal to 6.614378278 and -6.614378278.Subproblem 1
x + 7.5 = 6.614378278 Simplifying x + 7.5 = 6.614378278 Reorder the terms: 7.5 + x = 6.614378278 Solving 7.5 + x = 6.614378278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 6.614378278 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.614378278 + -7.5 x = 6.614378278 + -7.5 Combine like terms: 6.614378278 + -7.5 = -0.885621722 x = -0.885621722 Simplifying x = -0.885621722Subproblem 2
x + 7.5 = -6.614378278 Simplifying x + 7.5 = -6.614378278 Reorder the terms: 7.5 + x = -6.614378278 Solving 7.5 + x = -6.614378278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -6.614378278 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.614378278 + -7.5 x = -6.614378278 + -7.5 Combine like terms: -6.614378278 + -7.5 = -14.114378278 x = -14.114378278 Simplifying x = -14.114378278Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.885621722, -14.114378278}
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