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Simplifying 5x2 + -32x + 20 = 0 Reorder the terms: 20 + -32x + 5x2 = 0 Solving 20 + -32x + 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'. 4 + -6.4x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6.4x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -6.4x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6.4x + x2 = 0 + -4 -6.4x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6.4x + x2 = -4 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 = -4 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = -4 + 10.24 Combine like terms: -4 + 10.24 = 6.24 10.24 + -6.4x + x2 = 6.24 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 6.24 Calculate the square root of the right side: 2.497999199 Break this problem into two subproblems by setting (x + -3.2) equal to 2.497999199 and -2.497999199.Subproblem 1
x + -3.2 = 2.497999199 Simplifying x + -3.2 = 2.497999199 Reorder the terms: -3.2 + x = 2.497999199 Solving -3.2 + x = 2.497999199 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 = 2.497999199 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 2.497999199 + 3.2 x = 2.497999199 + 3.2 Combine like terms: 2.497999199 + 3.2 = 5.697999199 x = 5.697999199 Simplifying x = 5.697999199Subproblem 2
x + -3.2 = -2.497999199 Simplifying x + -3.2 = -2.497999199 Reorder the terms: -3.2 + x = -2.497999199 Solving -3.2 + x = -2.497999199 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 = -2.497999199 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -2.497999199 + 3.2 x = -2.497999199 + 3.2 Combine like terms: -2.497999199 + 3.2 = 0.702000801 x = 0.702000801 Simplifying x = 0.702000801Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.697999199, 0.702000801}
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