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Simplifying 10x2 + -25x + 13 = 0 Reorder the terms: 13 + -25x + 10x2 = 0 Solving 13 + -25x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.3 + -2.5x + x2 = 0 Move the constant term to the right: Add '-1.3' to each side of the equation. 1.3 + -2.5x + -1.3 + x2 = 0 + -1.3 Reorder the terms: 1.3 + -1.3 + -2.5x + x2 = 0 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + -2.5x + x2 = 0 + -1.3 -2.5x + x2 = 0 + -1.3 Combine like terms: 0 + -1.3 = -1.3 -2.5x + x2 = -1.3 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -1.3 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.3 + 1.5625 Combine like terms: -1.3 + 1.5625 = 0.2625 1.5625 + -2.5x + x2 = 0.2625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.2625 Calculate the square root of the right side: 0.512347538 Break this problem into two subproblems by setting (x + -1.25) equal to 0.512347538 and -0.512347538.Subproblem 1
x + -1.25 = 0.512347538 Simplifying x + -1.25 = 0.512347538 Reorder the terms: -1.25 + x = 0.512347538 Solving -1.25 + x = 0.512347538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.512347538 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.512347538 + 1.25 x = 0.512347538 + 1.25 Combine like terms: 0.512347538 + 1.25 = 1.762347538 x = 1.762347538 Simplifying x = 1.762347538Subproblem 2
x + -1.25 = -0.512347538 Simplifying x + -1.25 = -0.512347538 Reorder the terms: -1.25 + x = -0.512347538 Solving -1.25 + x = -0.512347538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.512347538 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.512347538 + 1.25 x = -0.512347538 + 1.25 Combine like terms: -0.512347538 + 1.25 = 0.737652462 x = 0.737652462 Simplifying x = 0.737652462Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.762347538, 0.737652462}
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