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Simplifying 625 = x2 + -96x Reorder the terms: 625 = -96x + x2 Solving 625 = -96x + x2 Solving for variable 'x'. Reorder the terms: 625 + 96x + -1x2 = -96x + 96x + x2 + -1x2 Combine like terms: -96x + 96x = 0 625 + 96x + -1x2 = 0 + x2 + -1x2 625 + 96x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 625 + 96x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -625 + -96x + x2 = 0 Move the constant term to the right: Add '625' to each side of the equation. -625 + -96x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + -96x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + -96x + x2 = 0 + 625 -96x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 -96x + x2 = 625 The x term is -96x. Take half its coefficient (-48). Square it (2304) and add it to both sides. Add '2304' to each side of the equation. -96x + 2304 + x2 = 625 + 2304 Reorder the terms: 2304 + -96x + x2 = 625 + 2304 Combine like terms: 625 + 2304 = 2929 2304 + -96x + x2 = 2929 Factor a perfect square on the left side: (x + -48)(x + -48) = 2929 Calculate the square root of the right side: 54.120236511 Break this problem into two subproblems by setting (x + -48) equal to 54.120236511 and -54.120236511.Subproblem 1
x + -48 = 54.120236511 Simplifying x + -48 = 54.120236511 Reorder the terms: -48 + x = 54.120236511 Solving -48 + x = 54.120236511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = 54.120236511 + 48 Combine like terms: -48 + 48 = 0 0 + x = 54.120236511 + 48 x = 54.120236511 + 48 Combine like terms: 54.120236511 + 48 = 102.120236511 x = 102.120236511 Simplifying x = 102.120236511Subproblem 2
x + -48 = -54.120236511 Simplifying x + -48 = -54.120236511 Reorder the terms: -48 + x = -54.120236511 Solving -48 + x = -54.120236511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = -54.120236511 + 48 Combine like terms: -48 + 48 = 0 0 + x = -54.120236511 + 48 x = -54.120236511 + 48 Combine like terms: -54.120236511 + 48 = -6.120236511 x = -6.120236511 Simplifying x = -6.120236511Solution
The solution to the problem is based on the solutions from the subproblems. x = {102.120236511, -6.120236511}
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