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Simplifying 196x2 + 84x + 18 = 0 Reorder the terms: 18 + 84x + 196x2 = 0 Solving 18 + 84x + 196x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 42x + 98x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 42x + 98x2)' equal to zero and attempt to solve: Simplifying 9 + 42x + 98x2 = 0 Solving 9 + 42x + 98x2 = 0 Begin completing the square. Divide all terms by 98 the coefficient of the squared term: Divide each side by '98'. 0.09183673469 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '-0.09183673469' to each side of the equation. 0.09183673469 + 0.4285714286x + -0.09183673469 + x2 = 0 + -0.09183673469 Reorder the terms: 0.09183673469 + -0.09183673469 + 0.4285714286x + x2 = 0 + -0.09183673469 Combine like terms: 0.09183673469 + -0.09183673469 = 0.00000000000 0.00000000000 + 0.4285714286x + x2 = 0 + -0.09183673469 0.4285714286x + x2 = 0 + -0.09183673469 Combine like terms: 0 + -0.09183673469 = -0.09183673469 0.4285714286x + x2 = -0.09183673469 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = -0.09183673469 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = -0.09183673469 + 0.04591836735 Combine like terms: -0.09183673469 + 0.04591836735 = -0.04591836734 0.04591836735 + 0.4285714286x + x2 = -0.04591836734 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = -0.04591836734 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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