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Simplifying 5x2 + -48x + -180 = 0 Reorder the terms: -180 + -48x + 5x2 = 0 Solving -180 + -48x + 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'. -36 + -9.6x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -9.6x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -9.6x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -9.6x + x2 = 0 + 36 -9.6x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -9.6x + x2 = 36 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = 36 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = 36 + 23.04 Combine like terms: 36 + 23.04 = 59.04 23.04 + -9.6x + x2 = 59.04 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 59.04 Calculate the square root of the right side: 7.683749085 Break this problem into two subproblems by setting (x + -4.8) equal to 7.683749085 and -7.683749085.Subproblem 1
x + -4.8 = 7.683749085 Simplifying x + -4.8 = 7.683749085 Reorder the terms: -4.8 + x = 7.683749085 Solving -4.8 + x = 7.683749085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 7.683749085 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 7.683749085 + 4.8 x = 7.683749085 + 4.8 Combine like terms: 7.683749085 + 4.8 = 12.483749085 x = 12.483749085 Simplifying x = 12.483749085Subproblem 2
x + -4.8 = -7.683749085 Simplifying x + -4.8 = -7.683749085 Reorder the terms: -4.8 + x = -7.683749085 Solving -4.8 + x = -7.683749085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -7.683749085 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -7.683749085 + 4.8 x = -7.683749085 + 4.8 Combine like terms: -7.683749085 + 4.8 = -2.883749085 x = -2.883749085 Simplifying x = -2.883749085Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.483749085, -2.883749085}
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