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Simplifying x2 + -96x + -51 = 0 Reorder the terms: -51 + -96x + x2 = 0 Solving -51 + -96x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -96x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -96x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -96x + x2 = 0 + 51 -96x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -96x + x2 = 51 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 = 51 + 2304 Reorder the terms: 2304 + -96x + x2 = 51 + 2304 Combine like terms: 51 + 2304 = 2355 2304 + -96x + x2 = 2355 Factor a perfect square on the left side: (x + -48)(x + -48) = 2355 Calculate the square root of the right side: 48.528342234 Break this problem into two subproblems by setting (x + -48) equal to 48.528342234 and -48.528342234.Subproblem 1
x + -48 = 48.528342234 Simplifying x + -48 = 48.528342234 Reorder the terms: -48 + x = 48.528342234 Solving -48 + x = 48.528342234 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 = 48.528342234 + 48 Combine like terms: -48 + 48 = 0 0 + x = 48.528342234 + 48 x = 48.528342234 + 48 Combine like terms: 48.528342234 + 48 = 96.528342234 x = 96.528342234 Simplifying x = 96.528342234Subproblem 2
x + -48 = -48.528342234 Simplifying x + -48 = -48.528342234 Reorder the terms: -48 + x = -48.528342234 Solving -48 + x = -48.528342234 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 = -48.528342234 + 48 Combine like terms: -48 + 48 = 0 0 + x = -48.528342234 + 48 x = -48.528342234 + 48 Combine like terms: -48.528342234 + 48 = -0.528342234 x = -0.528342234 Simplifying x = -0.528342234Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.528342234, -0.528342234}
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