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Simplifying 2x2 + -3x + -96 = 0 Reorder the terms: -96 + -3x + 2x2 = 0 Solving -96 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -48 + -1.5x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -1.5x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -1.5x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -1.5x + x2 = 0 + 48 -1.5x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -1.5x + x2 = 48 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 48 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 48 + 0.5625 Combine like terms: 48 + 0.5625 = 48.5625 0.5625 + -1.5x + x2 = 48.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 48.5625 Calculate the square root of the right side: 6.968679932 Break this problem into two subproblems by setting (x + -0.75) equal to 6.968679932 and -6.968679932.Subproblem 1
x + -0.75 = 6.968679932 Simplifying x + -0.75 = 6.968679932 Reorder the terms: -0.75 + x = 6.968679932 Solving -0.75 + x = 6.968679932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 6.968679932 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 6.968679932 + 0.75 x = 6.968679932 + 0.75 Combine like terms: 6.968679932 + 0.75 = 7.718679932 x = 7.718679932 Simplifying x = 7.718679932Subproblem 2
x + -0.75 = -6.968679932 Simplifying x + -0.75 = -6.968679932 Reorder the terms: -0.75 + x = -6.968679932 Solving -0.75 + x = -6.968679932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -6.968679932 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -6.968679932 + 0.75 x = -6.968679932 + 0.75 Combine like terms: -6.968679932 + 0.75 = -6.218679932 x = -6.218679932 Simplifying x = -6.218679932Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.718679932, -6.218679932}
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