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Simplifying 5x2 + -48x + 2 = 0 Reorder the terms: 2 + -48x + 5x2 = 0 Solving 2 + -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'. 0.4 + -9.6x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -9.6x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -9.6x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -9.6x + x2 = 0 + -0.4 -9.6x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -9.6x + x2 = -0.4 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 = -0.4 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = -0.4 + 23.04 Combine like terms: -0.4 + 23.04 = 22.64 23.04 + -9.6x + x2 = 22.64 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 22.64 Calculate the square root of the right side: 4.758150901 Break this problem into two subproblems by setting (x + -4.8) equal to 4.758150901 and -4.758150901.Subproblem 1
x + -4.8 = 4.758150901 Simplifying x + -4.8 = 4.758150901 Reorder the terms: -4.8 + x = 4.758150901 Solving -4.8 + x = 4.758150901 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 = 4.758150901 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 4.758150901 + 4.8 x = 4.758150901 + 4.8 Combine like terms: 4.758150901 + 4.8 = 9.558150901 x = 9.558150901 Simplifying x = 9.558150901Subproblem 2
x + -4.8 = -4.758150901 Simplifying x + -4.8 = -4.758150901 Reorder the terms: -4.8 + x = -4.758150901 Solving -4.8 + x = -4.758150901 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 = -4.758150901 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -4.758150901 + 4.8 x = -4.758150901 + 4.8 Combine like terms: -4.758150901 + 4.8 = 0.041849099 x = 0.041849099 Simplifying x = 0.041849099Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.558150901, 0.041849099}
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