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Simplifying 5x2 + -44x + -96 = 0 Reorder the terms: -96 + -44x + 5x2 = 0 Solving -96 + -44x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.2 + -8.8x + x2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -8.8x + 19.2 + x2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -8.8x + x2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -8.8x + x2 = 0 + 19.2 -8.8x + x2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -8.8x + x2 = 19.2 The x term is -8.8x. Take half its coefficient (-4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. -8.8x + 19.36 + x2 = 19.2 + 19.36 Reorder the terms: 19.36 + -8.8x + x2 = 19.2 + 19.36 Combine like terms: 19.2 + 19.36 = 38.56 19.36 + -8.8x + x2 = 38.56 Factor a perfect square on the left side: (x + -4.4)(x + -4.4) = 38.56 Calculate the square root of the right side: 6.209669879 Break this problem into two subproblems by setting (x + -4.4) equal to 6.209669879 and -6.209669879.Subproblem 1
x + -4.4 = 6.209669879 Simplifying x + -4.4 = 6.209669879 Reorder the terms: -4.4 + x = 6.209669879 Solving -4.4 + x = 6.209669879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = 6.209669879 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = 6.209669879 + 4.4 x = 6.209669879 + 4.4 Combine like terms: 6.209669879 + 4.4 = 10.609669879 x = 10.609669879 Simplifying x = 10.609669879Subproblem 2
x + -4.4 = -6.209669879 Simplifying x + -4.4 = -6.209669879 Reorder the terms: -4.4 + x = -6.209669879 Solving -4.4 + x = -6.209669879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = -6.209669879 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = -6.209669879 + 4.4 x = -6.209669879 + 4.4 Combine like terms: -6.209669879 + 4.4 = -1.809669879 x = -1.809669879 Simplifying x = -1.809669879Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.609669879, -1.809669879}
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