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Simplifying 172x = 336x2 + 24 Reorder the terms: 172x = 24 + 336x2 Solving 172x = 24 + 336x2 Solving for variable 'x'. Reorder the terms: -24 + 172x + -336x2 = 24 + 336x2 + -24 + -336x2 Reorder the terms: -24 + 172x + -336x2 = 24 + -24 + 336x2 + -336x2 Combine like terms: 24 + -24 = 0 -24 + 172x + -336x2 = 0 + 336x2 + -336x2 -24 + 172x + -336x2 = 336x2 + -336x2 Combine like terms: 336x2 + -336x2 = 0 -24 + 172x + -336x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 43x + -84x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + 43x + -84x2)' equal to zero and attempt to solve: Simplifying -6 + 43x + -84x2 = 0 Solving -6 + 43x + -84x2 = 0 Begin completing the square. Divide all terms by -84 the coefficient of the squared term: Divide each side by '-84'. 0.07142857143 + -0.5119047619x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + -0.5119047619x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + -0.5119047619x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + -0.5119047619x + x2 = 0 + -0.07142857143 -0.5119047619x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 -0.5119047619x + x2 = -0.07142857143 The x term is -0.5119047619x. Take half its coefficient (-0.255952381). Square it (0.06551162134) and add it to both sides. Add '0.06551162134' to each side of the equation. -0.5119047619x + 0.06551162134 + x2 = -0.07142857143 + 0.06551162134 Reorder the terms: 0.06551162134 + -0.5119047619x + x2 = -0.07142857143 + 0.06551162134 Combine like terms: -0.07142857143 + 0.06551162134 = -0.00591695009 0.06551162134 + -0.5119047619x + x2 = -0.00591695009 Factor a perfect square on the left side: (x + -0.255952381)(x + -0.255952381) = -0.00591695009 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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