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Simplifying 0 = 2.52 + -1(4.8x) + -1(0.800x2) Remove parenthesis around (4.8x) 0 = 2.52 + -1 * 4.8x + -1(0.800x2) Multiply -1 * 4.8 0 = 2.52 + -4.8x + -1(0.800x2) Remove parenthesis around (0.800x2) 0 = 2.52 + -4.8x + -1 * 0.800x2 Multiply -1 * 0.800 0 = 2.52 + -4.8x + -0.8x2 Solving 0 = 2.52 + -4.8x + -0.8x2 Solving for variable 'x'. Combine like terms: 0 + -2.52 = -2.52 -2.52 + 4.8x + 0.8x2 = 2.52 + -4.8x + -0.8x2 + -2.52 + 4.8x + 0.8x2 Reorder the terms: -2.52 + 4.8x + 0.8x2 = 2.52 + -2.52 + -4.8x + 4.8x + -0.8x2 + 0.8x2 Combine like terms: 2.52 + -2.52 = 0.00 -2.52 + 4.8x + 0.8x2 = 0.00 + -4.8x + 4.8x + -0.8x2 + 0.8x2 -2.52 + 4.8x + 0.8x2 = -4.8x + 4.8x + -0.8x2 + 0.8x2 Combine like terms: -4.8x + 4.8x = 0.0 -2.52 + 4.8x + 0.8x2 = 0.0 + -0.8x2 + 0.8x2 -2.52 + 4.8x + 0.8x2 = -0.8x2 + 0.8x2 Combine like terms: -0.8x2 + 0.8x2 = 0.0 -2.52 + 4.8x + 0.8x2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -3.15 + 6x + x2 = 0 Move the constant term to the right: Add '3.15' to each side of the equation. -3.15 + 6x + 3.15 + x2 = 0 + 3.15 Reorder the terms: -3.15 + 3.15 + 6x + x2 = 0 + 3.15 Combine like terms: -3.15 + 3.15 = 0.00 0.00 + 6x + x2 = 0 + 3.15 6x + x2 = 0 + 3.15 Combine like terms: 0 + 3.15 = 3.15 6x + x2 = 3.15 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 3.15 + 9 Reorder the terms: 9 + 6x + x2 = 3.15 + 9 Combine like terms: 3.15 + 9 = 12.15 9 + 6x + x2 = 12.15 Factor a perfect square on the left side: (x + 3)(x + 3) = 12.15 Calculate the square root of the right side: 3.485685012 Break this problem into two subproblems by setting (x + 3) equal to 3.485685012 and -3.485685012.Subproblem 1
x + 3 = 3.485685012 Simplifying x + 3 = 3.485685012 Reorder the terms: 3 + x = 3.485685012 Solving 3 + x = 3.485685012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.485685012 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.485685012 + -3 x = 3.485685012 + -3 Combine like terms: 3.485685012 + -3 = 0.485685012 x = 0.485685012 Simplifying x = 0.485685012Subproblem 2
x + 3 = -3.485685012 Simplifying x + 3 = -3.485685012 Reorder the terms: 3 + x = -3.485685012 Solving 3 + x = -3.485685012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.485685012 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.485685012 + -3 x = -3.485685012 + -3 Combine like terms: -3.485685012 + -3 = -6.485685012 x = -6.485685012 Simplifying x = -6.485685012Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.485685012, -6.485685012}
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