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Simplifying 25x2 + 15x + 1 = 0 Reorder the terms: 1 + 15x + 25x2 = 0 Solving 1 + 15x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.04 + 0.6x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 0.6x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 0.6x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 0.6x + x2 = 0 + -0.04 0.6x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 0.6x + x2 = -0.04 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = -0.04 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = -0.04 + 0.09 Combine like terms: -0.04 + 0.09 = 0.05 0.09 + 0.6x + x2 = 0.05 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.05 Calculate the square root of the right side: 0.223606798 Break this problem into two subproblems by setting (x + 0.3) equal to 0.223606798 and -0.223606798.Subproblem 1
x + 0.3 = 0.223606798 Simplifying x + 0.3 = 0.223606798 Reorder the terms: 0.3 + x = 0.223606798 Solving 0.3 + x = 0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.223606798 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.223606798 + -0.3 x = 0.223606798 + -0.3 Combine like terms: 0.223606798 + -0.3 = -0.076393202 x = -0.076393202 Simplifying x = -0.076393202Subproblem 2
x + 0.3 = -0.223606798 Simplifying x + 0.3 = -0.223606798 Reorder the terms: 0.3 + x = -0.223606798 Solving 0.3 + x = -0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.223606798 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.223606798 + -0.3 x = -0.223606798 + -0.3 Combine like terms: -0.223606798 + -0.3 = -0.523606798 x = -0.523606798 Simplifying x = -0.523606798Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.076393202, -0.523606798}
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