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Simplifying 6x2 + 28x + 196 = 0 Reorder the terms: 196 + 28x + 6x2 = 0 Solving 196 + 28x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(98 + 14x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(98 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying 98 + 14x + 3x2 = 0 Solving 98 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 32.66666667 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '-32.66666667' to each side of the equation. 32.66666667 + 4.666666667x + -32.66666667 + x2 = 0 + -32.66666667 Reorder the terms: 32.66666667 + -32.66666667 + 4.666666667x + x2 = 0 + -32.66666667 Combine like terms: 32.66666667 + -32.66666667 = 0.00000000 0.00000000 + 4.666666667x + x2 = 0 + -32.66666667 4.666666667x + x2 = 0 + -32.66666667 Combine like terms: 0 + -32.66666667 = -32.66666667 4.666666667x + x2 = -32.66666667 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = -32.66666667 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = -32.66666667 + 5.444444448 Combine like terms: -32.66666667 + 5.444444448 = -27.222222222 5.444444448 + 4.666666667x + x2 = -27.222222222 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = -27.222222222 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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