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Simplifying x2 + -9.6x + 23.04 = 0 Reorder the terms: 23.04 + -9.6x + x2 = 0 Solving 23.04 + -9.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23.04' to each side of the equation. 23.04 + -9.6x + -23.04 + x2 = 0 + -23.04 Reorder the terms: 23.04 + -23.04 + -9.6x + x2 = 0 + -23.04 Combine like terms: 23.04 + -23.04 = 0.00 0.00 + -9.6x + x2 = 0 + -23.04 -9.6x + x2 = 0 + -23.04 Combine like terms: 0 + -23.04 = -23.04 -9.6x + x2 = -23.04 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = -23.04 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = -23.04 + 23.04 Combine like terms: -23.04 + 23.04 = 0.00 23.04 + -9.6x + x2 = 0.00 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -4.8) equal to 0.00 and 0.00.Subproblem 1
x + -4.8 = 0.00 Simplifying x + -4.8 = 0.00 Reorder the terms: -4.8 + x = 0.00 Solving -4.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 0.00 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 0.00 + 4.8 x = 0.00 + 4.8 Combine like terms: 0.00 + 4.8 = 4.8 x = 4.8 Simplifying x = 4.8Subproblem 2
x + -4.8 = 0.00 Simplifying x + -4.8 = 0.00 Reorder the terms: -4.8 + x = 0.00 Solving -4.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 0.00 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 0.00 + 4.8 x = 0.00 + 4.8 Combine like terms: 0.00 + 4.8 = 4.8 x = 4.8 Simplifying x = 4.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8, 4.8}
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