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Simplifying 5x2 + -48x + 60 = 0 Reorder the terms: 60 + -48x + 5x2 = 0 Solving 60 + -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'. 12 + -9.6x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -9.6x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -9.6x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -9.6x + x2 = 0 + -12 -9.6x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -9.6x + x2 = -12 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 = -12 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = -12 + 23.04 Combine like terms: -12 + 23.04 = 11.04 23.04 + -9.6x + x2 = 11.04 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 11.04 Calculate the square root of the right side: 3.322649545 Break this problem into two subproblems by setting (x + -4.8) equal to 3.322649545 and -3.322649545.Subproblem 1
x + -4.8 = 3.322649545 Simplifying x + -4.8 = 3.322649545 Reorder the terms: -4.8 + x = 3.322649545 Solving -4.8 + x = 3.322649545 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 = 3.322649545 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 3.322649545 + 4.8 x = 3.322649545 + 4.8 Combine like terms: 3.322649545 + 4.8 = 8.122649545 x = 8.122649545 Simplifying x = 8.122649545Subproblem 2
x + -4.8 = -3.322649545 Simplifying x + -4.8 = -3.322649545 Reorder the terms: -4.8 + x = -3.322649545 Solving -4.8 + x = -3.322649545 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 = -3.322649545 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -3.322649545 + 4.8 x = -3.322649545 + 4.8 Combine like terms: -3.322649545 + 4.8 = 1.477350455 x = 1.477350455 Simplifying x = 1.477350455Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.122649545, 1.477350455}
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