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Simplifying 0.3x2 + -48x + 24 = 0 Reorder the terms: 24 + -48x + 0.3x2 = 0 Solving 24 + -48x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 80 + -160x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -160x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -160x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -160x + x2 = 0 + -80 -160x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -160x + x2 = -80 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = -80 + 6400 Reorder the terms: 6400 + -160x + x2 = -80 + 6400 Combine like terms: -80 + 6400 = 6320 6400 + -160x + x2 = 6320 Factor a perfect square on the left side: (x + -80)(x + -80) = 6320 Calculate the square root of the right side: 79.498427657 Break this problem into two subproblems by setting (x + -80) equal to 79.498427657 and -79.498427657.Subproblem 1
x + -80 = 79.498427657 Simplifying x + -80 = 79.498427657 Reorder the terms: -80 + x = 79.498427657 Solving -80 + x = 79.498427657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 79.498427657 + 80 Combine like terms: -80 + 80 = 0 0 + x = 79.498427657 + 80 x = 79.498427657 + 80 Combine like terms: 79.498427657 + 80 = 159.498427657 x = 159.498427657 Simplifying x = 159.498427657Subproblem 2
x + -80 = -79.498427657 Simplifying x + -80 = -79.498427657 Reorder the terms: -80 + x = -79.498427657 Solving -80 + x = -79.498427657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -79.498427657 + 80 Combine like terms: -80 + 80 = 0 0 + x = -79.498427657 + 80 x = -79.498427657 + 80 Combine like terms: -79.498427657 + 80 = 0.501572343 x = 0.501572343 Simplifying x = 0.501572343Solution
The solution to the problem is based on the solutions from the subproblems. x = {159.498427657, 0.501572343}
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