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Simplifying 5x2 + -25x + 12 = 0 Reorder the terms: 12 + -25x + 5x2 = 0 Solving 12 + -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'. 2.4 + -5x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -5x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -5x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -5x + x2 = 0 + -2.4 -5x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -5x + x2 = -2.4 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 = -2.4 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2.4 + 6.25 Combine like terms: -2.4 + 6.25 = 3.85 6.25 + -5x + x2 = 3.85 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3.85 Calculate the square root of the right side: 1.962141687 Break this problem into two subproblems by setting (x + -2.5) equal to 1.962141687 and -1.962141687.Subproblem 1
x + -2.5 = 1.962141687 Simplifying x + -2.5 = 1.962141687 Reorder the terms: -2.5 + x = 1.962141687 Solving -2.5 + x = 1.962141687 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 = 1.962141687 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.962141687 + 2.5 x = 1.962141687 + 2.5 Combine like terms: 1.962141687 + 2.5 = 4.462141687 x = 4.462141687 Simplifying x = 4.462141687Subproblem 2
x + -2.5 = -1.962141687 Simplifying x + -2.5 = -1.962141687 Reorder the terms: -2.5 + x = -1.962141687 Solving -2.5 + x = -1.962141687 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 = -1.962141687 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.962141687 + 2.5 x = -1.962141687 + 2.5 Combine like terms: -1.962141687 + 2.5 = 0.537858313 x = 0.537858313 Simplifying x = 0.537858313Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.462141687, 0.537858313}
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