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Simplifying x2 + x + -48 = 48 Reorder the terms: -48 + x + x2 = 48 Solving -48 + x + x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + -48 + x + x2 = 48 + -48 Combine like terms: -48 + -48 = -96 -96 + x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -96 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + x + x2 = 0 + 96 x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 x + x2 = 96 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 96 + 0.25 Reorder the terms: 0.25 + x + x2 = 96 + 0.25 Combine like terms: 96 + 0.25 = 96.25 0.25 + x + x2 = 96.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 0.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 0.5 = 9.810708435 Simplifying x + 0.5 = 9.810708435 Reorder the terms: 0.5 + x = 9.810708435 Solving 0.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.810708435 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.810708435 + -0.5 x = 9.810708435 + -0.5 Combine like terms: 9.810708435 + -0.5 = 9.310708435 x = 9.310708435 Simplifying x = 9.310708435Subproblem 2
x + 0.5 = -9.810708435 Simplifying x + 0.5 = -9.810708435 Reorder the terms: 0.5 + x = -9.810708435 Solving 0.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.810708435 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.810708435 + -0.5 x = -9.810708435 + -0.5 Combine like terms: -9.810708435 + -0.5 = -10.310708435 x = -10.310708435 Simplifying x = -10.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.310708435, -10.310708435}
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