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Simplifying 25x2 + -60x + 16 = 0 Reorder the terms: 16 + -60x + 25x2 = 0 Solving 16 + -60x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.64 + -2.4x + x2 = 0 Move the constant term to the right: Add '-0.64' to each side of the equation. 0.64 + -2.4x + -0.64 + x2 = 0 + -0.64 Reorder the terms: 0.64 + -0.64 + -2.4x + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + -2.4x + x2 = 0 + -0.64 -2.4x + x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 -2.4x + x2 = -0.64 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.64 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.64 + 1.44 Combine like terms: -0.64 + 1.44 = 0.8 1.44 + -2.4x + x2 = 0.8 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (x + -1.2) equal to 0.894427191 and -0.894427191.Subproblem 1
x + -1.2 = 0.894427191 Simplifying x + -1.2 = 0.894427191 Reorder the terms: -1.2 + x = 0.894427191 Solving -1.2 + x = 0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.894427191 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.894427191 + 1.2 x = 0.894427191 + 1.2 Combine like terms: 0.894427191 + 1.2 = 2.094427191 x = 2.094427191 Simplifying x = 2.094427191Subproblem 2
x + -1.2 = -0.894427191 Simplifying x + -1.2 = -0.894427191 Reorder the terms: -1.2 + x = -0.894427191 Solving -1.2 + x = -0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.894427191 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.894427191 + 1.2 x = -0.894427191 + 1.2 Combine like terms: -0.894427191 + 1.2 = 0.305572809 x = 0.305572809 Simplifying x = 0.305572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.094427191, 0.305572809}
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