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Simplifying 14x2 + 8x + 16 = 0 Reorder the terms: 16 + 8x + 14x2 = 0 Solving 16 + 8x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 4x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 4x + 7x2)' equal to zero and attempt to solve: Simplifying 8 + 4x + 7x2 = 0 Solving 8 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.142857143 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + 0.5714285714x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + 0.5714285714x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + -1.142857143 0.5714285714x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 0.5714285714x + x2 = -1.142857143 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 = -1.142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = -1.142857143 + 0.08163265305 Combine like terms: -1.142857143 + 0.08163265305 = -1.06122448995 0.08163265305 + 0.5714285714x + x2 = -1.06122448995 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = -1.06122448995 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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