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Simplifying 2x2 + 24x + -25 = 0 Reorder the terms: -25 + 24x + 2x2 = 0 Solving -25 + 24x + 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 + 12x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 12x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 12x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 12x + x2 = 0 + 12.5 12x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 12x + x2 = 12.5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 12.5 + 36 Reorder the terms: 36 + 12x + x2 = 12.5 + 36 Combine like terms: 12.5 + 36 = 48.5 36 + 12x + x2 = 48.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 48.5 Calculate the square root of the right side: 6.964194139 Break this problem into two subproblems by setting (x + 6) equal to 6.964194139 and -6.964194139.Subproblem 1
x + 6 = 6.964194139 Simplifying x + 6 = 6.964194139 Reorder the terms: 6 + x = 6.964194139 Solving 6 + x = 6.964194139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.964194139 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.964194139 + -6 x = 6.964194139 + -6 Combine like terms: 6.964194139 + -6 = 0.964194139 x = 0.964194139 Simplifying x = 0.964194139Subproblem 2
x + 6 = -6.964194139 Simplifying x + 6 = -6.964194139 Reorder the terms: 6 + x = -6.964194139 Solving 6 + x = -6.964194139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.964194139 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.964194139 + -6 x = -6.964194139 + -6 Combine like terms: -6.964194139 + -6 = -12.964194139 x = -12.964194139 Simplifying x = -12.964194139Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.964194139, -12.964194139}
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