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Simplifying 0 = -4.9x2 + 24.5x + 8.5 Reorder the terms: 0 = 8.5 + 24.5x + -4.9x2 Solving 0 = 8.5 + 24.5x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -8.5 = -8.5 -8.5 + -24.5x + 4.9x2 = 8.5 + 24.5x + -4.9x2 + -8.5 + -24.5x + 4.9x2 Reorder the terms: -8.5 + -24.5x + 4.9x2 = 8.5 + -8.5 + 24.5x + -24.5x + -4.9x2 + 4.9x2 Combine like terms: 8.5 + -8.5 = 0.0 -8.5 + -24.5x + 4.9x2 = 0.0 + 24.5x + -24.5x + -4.9x2 + 4.9x2 -8.5 + -24.5x + 4.9x2 = 24.5x + -24.5x + -4.9x2 + 4.9x2 Combine like terms: 24.5x + -24.5x = 0.0 -8.5 + -24.5x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -8.5 + -24.5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -8.5 + -24.5x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.734693878 + -5x + x2 = 0 Move the constant term to the right: Add '1.734693878' to each side of the equation. -1.734693878 + -5x + 1.734693878 + x2 = 0 + 1.734693878 Reorder the terms: -1.734693878 + 1.734693878 + -5x + x2 = 0 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + -5x + x2 = 0 + 1.734693878 -5x + x2 = 0 + 1.734693878 Combine like terms: 0 + 1.734693878 = 1.734693878 -5x + x2 = 1.734693878 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1.734693878 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.734693878 + 6.25 Combine like terms: 1.734693878 + 6.25 = 7.984693878 6.25 + -5x + x2 = 7.984693878 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.984693878 Calculate the square root of the right side: 2.825720064 Break this problem into two subproblems by setting (x + -2.5) equal to 2.825720064 and -2.825720064.Subproblem 1
x + -2.5 = 2.825720064 Simplifying x + -2.5 = 2.825720064 Reorder the terms: -2.5 + x = 2.825720064 Solving -2.5 + x = 2.825720064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.825720064 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.825720064 + 2.5 x = 2.825720064 + 2.5 Combine like terms: 2.825720064 + 2.5 = 5.325720064 x = 5.325720064 Simplifying x = 5.325720064Subproblem 2
x + -2.5 = -2.825720064 Simplifying x + -2.5 = -2.825720064 Reorder the terms: -2.5 + x = -2.825720064 Solving -2.5 + x = -2.825720064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.825720064 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.825720064 + 2.5 x = -2.825720064 + 2.5 Combine like terms: -2.825720064 + 2.5 = -0.325720064 x = -0.325720064 Simplifying x = -0.325720064Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.325720064, -0.325720064}
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