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Simplifying 2x2 + 25x + 15 = 0 Reorder the terms: 15 + 25x + 2x2 = 0 Solving 15 + 25x + 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'. 7.5 + 12.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 12.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 12.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 12.5x + x2 = 0 + -7.5 12.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 12.5x + x2 = -7.5 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = -7.5 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = -7.5 + 39.0625 Combine like terms: -7.5 + 39.0625 = 31.5625 39.0625 + 12.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + 6.25) equal to 5.618051264 and -5.618051264.Subproblem 1
x + 6.25 = 5.618051264 Simplifying x + 6.25 = 5.618051264 Reorder the terms: 6.25 + x = 5.618051264 Solving 6.25 + x = 5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 5.618051264 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 5.618051264 + -6.25 x = 5.618051264 + -6.25 Combine like terms: 5.618051264 + -6.25 = -0.631948736 x = -0.631948736 Simplifying x = -0.631948736Subproblem 2
x + 6.25 = -5.618051264 Simplifying x + 6.25 = -5.618051264 Reorder the terms: 6.25 + x = -5.618051264 Solving 6.25 + x = -5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -5.618051264 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -5.618051264 + -6.25 x = -5.618051264 + -6.25 Combine like terms: -5.618051264 + -6.25 = -11.868051264 x = -11.868051264 Simplifying x = -11.868051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.631948736, -11.868051264}
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