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Simplifying x2 + -96x + -768 = 0 Reorder the terms: -768 + -96x + x2 = 0 Solving -768 + -96x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '768' to each side of the equation. -768 + -96x + 768 + x2 = 0 + 768 Reorder the terms: -768 + 768 + -96x + x2 = 0 + 768 Combine like terms: -768 + 768 = 0 0 + -96x + x2 = 0 + 768 -96x + x2 = 0 + 768 Combine like terms: 0 + 768 = 768 -96x + x2 = 768 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 = 768 + 2304 Reorder the terms: 2304 + -96x + x2 = 768 + 2304 Combine like terms: 768 + 2304 = 3072 2304 + -96x + x2 = 3072 Factor a perfect square on the left side: (x + -48)(x + -48) = 3072 Calculate the square root of the right side: 55.425625842 Break this problem into two subproblems by setting (x + -48) equal to 55.425625842 and -55.425625842.Subproblem 1
x + -48 = 55.425625842 Simplifying x + -48 = 55.425625842 Reorder the terms: -48 + x = 55.425625842 Solving -48 + x = 55.425625842 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 = 55.425625842 + 48 Combine like terms: -48 + 48 = 0 0 + x = 55.425625842 + 48 x = 55.425625842 + 48 Combine like terms: 55.425625842 + 48 = 103.425625842 x = 103.425625842 Simplifying x = 103.425625842Subproblem 2
x + -48 = -55.425625842 Simplifying x + -48 = -55.425625842 Reorder the terms: -48 + x = -55.425625842 Solving -48 + x = -55.425625842 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 = -55.425625842 + 48 Combine like terms: -48 + 48 = 0 0 + x = -55.425625842 + 48 x = -55.425625842 + 48 Combine like terms: -55.425625842 + 48 = -7.425625842 x = -7.425625842 Simplifying x = -7.425625842Solution
The solution to the problem is based on the solutions from the subproblems. x = {103.425625842, -7.425625842}
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