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Simplifying 2.5x2 + -16x + 22.5 = 0 Reorder the terms: 22.5 + -16x + 2.5x2 = 0 Solving 22.5 + -16x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 9 + -6.4x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -6.4x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -6.4x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -6.4x + x2 = 0 + -9 -6.4x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -6.4x + x2 = -9 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 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = -9 + 10.24 Combine like terms: -9 + 10.24 = 1.24 10.24 + -6.4x + x2 = 1.24 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + -3.2) equal to 1.113552873 and -1.113552873.Subproblem 1
x + -3.2 = 1.113552873 Simplifying x + -3.2 = 1.113552873 Reorder the terms: -3.2 + x = 1.113552873 Solving -3.2 + x = 1.113552873 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 = 1.113552873 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 1.113552873 + 3.2 x = 1.113552873 + 3.2 Combine like terms: 1.113552873 + 3.2 = 4.313552873 x = 4.313552873 Simplifying x = 4.313552873Subproblem 2
x + -3.2 = -1.113552873 Simplifying x + -3.2 = -1.113552873 Reorder the terms: -3.2 + x = -1.113552873 Solving -3.2 + x = -1.113552873 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 = -1.113552873 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -1.113552873 + 3.2 x = -1.113552873 + 3.2 Combine like terms: -1.113552873 + 3.2 = 2.086447127 x = 2.086447127 Simplifying x = 2.086447127Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.313552873, 2.086447127}
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