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Simplifying 9.6x + 19.2 = x2 + 4x Reorder the terms: 19.2 + 9.6x = x2 + 4x Reorder the terms: 19.2 + 9.6x = 4x + x2 Solving 19.2 + 9.6x = 4x + x2 Solving for variable 'x'. Combine like terms: 9.6x + -4x = 5.6x 19.2 + 5.6x + -1x2 = 4x + x2 + -4x + -1x2 Reorder the terms: 19.2 + 5.6x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 19.2 + 5.6x + -1x2 = 0 + x2 + -1x2 19.2 + 5.6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 19.2 + 5.6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19.2 + -5.6x + x2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -5.6x + 19.2 + x2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -5.6x + x2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -5.6x + x2 = 0 + 19.2 -5.6x + x2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -5.6x + x2 = 19.2 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 19.2 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 19.2 + 7.84 Combine like terms: 19.2 + 7.84 = 27.04 7.84 + -5.6x + x2 = 27.04 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 27.04 Calculate the square root of the right side: 5.2 Break this problem into two subproblems by setting (x + -2.8) equal to 5.2 and -5.2.Subproblem 1
x + -2.8 = 5.2 Simplifying x + -2.8 = 5.2 Reorder the terms: -2.8 + x = 5.2 Solving -2.8 + x = 5.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 5.2 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 5.2 + 2.8 x = 5.2 + 2.8 Combine like terms: 5.2 + 2.8 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -2.8 = -5.2 Simplifying x + -2.8 = -5.2 Reorder the terms: -2.8 + x = -5.2 Solving -2.8 + x = -5.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -5.2 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -5.2 + 2.8 x = -5.2 + 2.8 Combine like terms: -5.2 + 2.8 = -2.4 x = -2.4 Simplifying x = -2.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -2.4}
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