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Simplifying x2 + -6.4x + 9.8 = 0 Reorder the terms: 9.8 + -6.4x + x2 = 0 Solving 9.8 + -6.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9.8' to each side of the equation. 9.8 + -6.4x + -9.8 + x2 = 0 + -9.8 Reorder the terms: 9.8 + -9.8 + -6.4x + x2 = 0 + -9.8 Combine like terms: 9.8 + -9.8 = 0.0 0.0 + -6.4x + x2 = 0 + -9.8 -6.4x + x2 = 0 + -9.8 Combine like terms: 0 + -9.8 = -9.8 -6.4x + x2 = -9.8 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = -9.8 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = -9.8 + 10.24 Combine like terms: -9.8 + 10.24 = 0.44 10.24 + -6.4x + x2 = 0.44 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + -3.2) equal to 0.663324958 and -0.663324958.Subproblem 1
x + -3.2 = 0.663324958 Simplifying x + -3.2 = 0.663324958 Reorder the terms: -3.2 + x = 0.663324958 Solving -3.2 + x = 0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 0.663324958 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 0.663324958 + 3.2 x = 0.663324958 + 3.2 Combine like terms: 0.663324958 + 3.2 = 3.863324958 x = 3.863324958 Simplifying x = 3.863324958Subproblem 2
x + -3.2 = -0.663324958 Simplifying x + -3.2 = -0.663324958 Reorder the terms: -3.2 + x = -0.663324958 Solving -3.2 + x = -0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -0.663324958 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -0.663324958 + 3.2 x = -0.663324958 + 3.2 Combine like terms: -0.663324958 + 3.2 = 2.536675042 x = 2.536675042 Simplifying x = 2.536675042Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.863324958, 2.536675042}
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