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Simplifying 5x2 + -15x + -192 = 0 Reorder the terms: -192 + -15x + 5x2 = 0 Solving -192 + -15x + 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'. -38.4 + -3x + x2 = 0 Move the constant term to the right: Add '38.4' to each side of the equation. -38.4 + -3x + 38.4 + x2 = 0 + 38.4 Reorder the terms: -38.4 + 38.4 + -3x + x2 = 0 + 38.4 Combine like terms: -38.4 + 38.4 = 0.0 0.0 + -3x + x2 = 0 + 38.4 -3x + x2 = 0 + 38.4 Combine like terms: 0 + 38.4 = 38.4 -3x + x2 = 38.4 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 38.4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 38.4 + 2.25 Combine like terms: 38.4 + 2.25 = 40.65 2.25 + -3x + x2 = 40.65 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 40.65 Calculate the square root of the right side: 6.375735252 Break this problem into two subproblems by setting (x + -1.5) equal to 6.375735252 and -6.375735252.Subproblem 1
x + -1.5 = 6.375735252 Simplifying x + -1.5 = 6.375735252 Reorder the terms: -1.5 + x = 6.375735252 Solving -1.5 + x = 6.375735252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.375735252 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.375735252 + 1.5 x = 6.375735252 + 1.5 Combine like terms: 6.375735252 + 1.5 = 7.875735252 x = 7.875735252 Simplifying x = 7.875735252Subproblem 2
x + -1.5 = -6.375735252 Simplifying x + -1.5 = -6.375735252 Reorder the terms: -1.5 + x = -6.375735252 Solving -1.5 + x = -6.375735252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.375735252 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.375735252 + 1.5 x = -6.375735252 + 1.5 Combine like terms: -6.375735252 + 1.5 = -4.875735252 x = -4.875735252 Simplifying x = -4.875735252Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.875735252, -4.875735252}
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