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Simplifying 4.8x2 + -21.6x + 9.6 = 0 Reorder the terms: 9.6 + -21.6x + 4.8x2 = 0 Solving 9.6 + -21.6x + 4.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.8 the coefficient of the squared term: Divide each side by '4.8'. 2 + -4.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4.5x + x2 = 0 + -2 -4.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4.5x + x2 = -2 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -2 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -2 + 5.0625 Combine like terms: -2 + 5.0625 = 3.0625 5.0625 + -4.5x + x2 = 3.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 3.0625 Calculate the square root of the right side: 1.75 Break this problem into two subproblems by setting (x + -2.25) equal to 1.75 and -1.75.Subproblem 1
x + -2.25 = 1.75 Simplifying x + -2.25 = 1.75 Reorder the terms: -2.25 + x = 1.75 Solving -2.25 + x = 1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.75 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.75 + 2.25 x = 1.75 + 2.25 Combine like terms: 1.75 + 2.25 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -2.25 = -1.75 Simplifying x + -2.25 = -1.75 Reorder the terms: -2.25 + x = -1.75 Solving -2.25 + x = -1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.75 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.75 + 2.25 x = -1.75 + 2.25 Combine like terms: -1.75 + 2.25 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, 0.5}
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