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Simplifying 5x2 + 25x + -3 = 0 Reorder the terms: -3 + 25x + 5x2 = 0 Solving -3 + 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'. -0.6 + 5x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 5x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 5x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 5x + x2 = 0 + 0.6 5x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 5x + x2 = 0.6 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 = 0.6 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.6 + 6.25 Combine like terms: 0.6 + 6.25 = 6.85 6.25 + 5x + x2 = 6.85 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.85 Calculate the square root of the right side: 2.617250466 Break this problem into two subproblems by setting (x + 2.5) equal to 2.617250466 and -2.617250466.Subproblem 1
x + 2.5 = 2.617250466 Simplifying x + 2.5 = 2.617250466 Reorder the terms: 2.5 + x = 2.617250466 Solving 2.5 + x = 2.617250466 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 = 2.617250466 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.617250466 + -2.5 x = 2.617250466 + -2.5 Combine like terms: 2.617250466 + -2.5 = 0.117250466 x = 0.117250466 Simplifying x = 0.117250466Subproblem 2
x + 2.5 = -2.617250466 Simplifying x + 2.5 = -2.617250466 Reorder the terms: 2.5 + x = -2.617250466 Solving 2.5 + x = -2.617250466 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 = -2.617250466 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.617250466 + -2.5 x = -2.617250466 + -2.5 Combine like terms: -2.617250466 + -2.5 = -5.117250466 x = -5.117250466 Simplifying x = -5.117250466Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.117250466, -5.117250466}
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