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Simplifying 8x2 + -48x + -50 = 0 Reorder the terms: -50 + -48x + 8x2 = 0 Solving -50 + -48x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -24x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -24x + 4x2)' equal to zero and attempt to solve: Simplifying -25 + -24x + 4x2 = 0 Solving -25 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -6x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -6x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -6x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -6x + x2 = 0 + 6.25 -6x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -6x + x2 = 6.25 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 6.25 + 9 Reorder the terms: 9 + -6x + x2 = 6.25 + 9 Combine like terms: 6.25 + 9 = 15.25 9 + -6x + x2 = 15.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -3) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -3 = 3.905124838 Simplifying x + -3 = 3.905124838 Reorder the terms: -3 + x = 3.905124838 Solving -3 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.905124838 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.905124838 + 3 x = 3.905124838 + 3 Combine like terms: 3.905124838 + 3 = 6.905124838 x = 6.905124838 Simplifying x = 6.905124838Subproblem 2
x + -3 = -3.905124838 Simplifying x + -3 = -3.905124838 Reorder the terms: -3 + x = -3.905124838 Solving -3 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.905124838 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.905124838 + 3 x = -3.905124838 + 3 Combine like terms: -3.905124838 + 3 = -0.905124838 x = -0.905124838 Simplifying x = -0.905124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.905124838, -0.905124838}Solution
x = {6.905124838, -0.905124838}
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