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Simplifying 5x2 + 25x + -2 = 0 Reorder the terms: -2 + 25x + 5x2 = 0 Solving -2 + 25x + 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'. -0.4 + 5x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 5x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 5x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 5x + x2 = 0 + 0.4 5x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 5x + x2 = 0.4 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.4 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.4 + 6.25 Combine like terms: 0.4 + 6.25 = 6.65 6.25 + 5x + x2 = 6.65 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.65 Calculate the square root of the right side: 2.578759392 Break this problem into two subproblems by setting (x + 2.5) equal to 2.578759392 and -2.578759392.Subproblem 1
x + 2.5 = 2.578759392 Simplifying x + 2.5 = 2.578759392 Reorder the terms: 2.5 + x = 2.578759392 Solving 2.5 + x = 2.578759392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.578759392 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.578759392 + -2.5 x = 2.578759392 + -2.5 Combine like terms: 2.578759392 + -2.5 = 0.078759392 x = 0.078759392 Simplifying x = 0.078759392Subproblem 2
x + 2.5 = -2.578759392 Simplifying x + 2.5 = -2.578759392 Reorder the terms: 2.5 + x = -2.578759392 Solving 2.5 + x = -2.578759392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.578759392 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.578759392 + -2.5 x = -2.578759392 + -2.5 Combine like terms: -2.578759392 + -2.5 = -5.078759392 x = -5.078759392 Simplifying x = -5.078759392Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.078759392, -5.078759392}
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