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Simplifying -48x2 + -8x + 168 = 0 Reorder the terms: 168 + -8x + -48x2 = 0 Solving 168 + -8x + -48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(21 + -1x + -6x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(21 + -1x + -6x2)' equal to zero and attempt to solve: Simplifying 21 + -1x + -6x2 = 0 Solving 21 + -1x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -3.5 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 0.1666666667x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 0.1666666667x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 0.1666666667x + x2 = 0 + 3.5 0.1666666667x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 0.1666666667x + x2 = 3.5 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 3.5 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 3.5 + 0.006944444447 Combine like terms: 3.5 + 0.006944444447 = 3.506944444447 0.006944444447 + 0.1666666667x + x2 = 3.506944444447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 3.506944444447 Calculate the square root of the right side: 1.872683755 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 1.872683755 and -1.872683755.Subproblem 1
x + 0.08333333335 = 1.872683755 Simplifying x + 0.08333333335 = 1.872683755 Reorder the terms: 0.08333333335 + x = 1.872683755 Solving 0.08333333335 + x = 1.872683755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 1.872683755 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 1.872683755 + -0.08333333335 x = 1.872683755 + -0.08333333335 Combine like terms: 1.872683755 + -0.08333333335 = 1.78935042165 x = 1.78935042165 Simplifying x = 1.78935042165Subproblem 2
x + 0.08333333335 = -1.872683755 Simplifying x + 0.08333333335 = -1.872683755 Reorder the terms: 0.08333333335 + x = -1.872683755 Solving 0.08333333335 + x = -1.872683755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -1.872683755 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -1.872683755 + -0.08333333335 x = -1.872683755 + -0.08333333335 Combine like terms: -1.872683755 + -0.08333333335 = -1.95601708835 x = -1.95601708835 Simplifying x = -1.95601708835Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.78935042165, -1.95601708835}Solution
x = {1.78935042165, -1.95601708835}
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