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Simplifying 49x2 + -28x + 14 = 0 Reorder the terms: 14 + -28x + 49x2 = 0 Solving 14 + -28x + 49x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(2 + -4x + 7x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(2 + -4x + 7x2)' equal to zero and attempt to solve: Simplifying 2 + -4x + 7x2 = 0 Solving 2 + -4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.5714285714x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -0.5714285714x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + -0.2857142857 -0.5714285714x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -0.5714285714x + x2 = -0.2857142857 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = -0.2857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = -0.2857142857 + 0.08163265305 Combine like terms: -0.2857142857 + 0.08163265305 = -0.20408163265 0.08163265305 + -0.5714285714x + x2 = -0.20408163265 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = -0.20408163265 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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