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Simplifying 25x2 + -30x + 9 = 96 Reorder the terms: 9 + -30x + 25x2 = 96 Solving 9 + -30x + 25x2 = 96 Solving for variable 'x'. Reorder the terms: 9 + -96 + -30x + 25x2 = 96 + -96 Combine like terms: 9 + -96 = -87 -87 + -30x + 25x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -87 + -30x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.48 + -1.2x + x2 = 0 Move the constant term to the right: Add '3.48' to each side of the equation. -3.48 + -1.2x + 3.48 + x2 = 0 + 3.48 Reorder the terms: -3.48 + 3.48 + -1.2x + x2 = 0 + 3.48 Combine like terms: -3.48 + 3.48 = 0.00 0.00 + -1.2x + x2 = 0 + 3.48 -1.2x + x2 = 0 + 3.48 Combine like terms: 0 + 3.48 = 3.48 -1.2x + x2 = 3.48 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 3.48 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 3.48 + 0.36 Combine like terms: 3.48 + 0.36 = 3.84 0.36 + -1.2x + x2 = 3.84 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (x + -0.6) equal to 1.959591794 and -1.959591794.Subproblem 1
x + -0.6 = 1.959591794 Simplifying x + -0.6 = 1.959591794 Reorder the terms: -0.6 + x = 1.959591794 Solving -0.6 + x = 1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.959591794 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.959591794 + 0.6 x = 1.959591794 + 0.6 Combine like terms: 1.959591794 + 0.6 = 2.559591794 x = 2.559591794 Simplifying x = 2.559591794Subproblem 2
x + -0.6 = -1.959591794 Simplifying x + -0.6 = -1.959591794 Reorder the terms: -0.6 + x = -1.959591794 Solving -0.6 + x = -1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.959591794 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.959591794 + 0.6 x = -1.959591794 + 0.6 Combine like terms: -1.959591794 + 0.6 = -1.359591794 x = -1.359591794 Simplifying x = -1.359591794Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.559591794, -1.359591794}
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