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Simplifying -0.7x2 + -3.5x + 16.8 = 0 Reorder the terms: 16.8 + -3.5x + -0.7x2 = 0 Solving 16.8 + -3.5x + -0.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -24 + 5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 5x + x2 = 0 + 24 5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 5x + x2 = 24 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 = 24 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 24 + 6.25 Combine like terms: 24 + 6.25 = 30.25 6.25 + 5x + x2 = 30.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 30.25 Calculate the square root of the right side: 5.5 Break this problem into two subproblems by setting (x + 2.5) equal to 5.5 and -5.5.Subproblem 1
x + 2.5 = 5.5 Simplifying x + 2.5 = 5.5 Reorder the terms: 2.5 + x = 5.5 Solving 2.5 + x = 5.5 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 = 5.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.5 + -2.5 x = 5.5 + -2.5 Combine like terms: 5.5 + -2.5 = 3 x = 3 Simplifying x = 3Subproblem 2
x + 2.5 = -5.5 Simplifying x + 2.5 = -5.5 Reorder the terms: 2.5 + x = -5.5 Solving 2.5 + x = -5.5 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 = -5.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.5 + -2.5 x = -5.5 + -2.5 Combine like terms: -5.5 + -2.5 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -8}
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