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Simplifying 6x2 + 10x + 30 = 0 Reorder the terms: 30 + 10x + 6x2 = 0 Solving 30 + 10x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying 15 + 5x + 3x2 = 0 Solving 15 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 1.666666667x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 1.666666667x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 1.666666667x + x2 = 0 + -5 1.666666667x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 1.666666667x + x2 = -5 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = -5 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -5 + 0.6944444447 Combine like terms: -5 + 0.6944444447 = -4.3055555553 0.6944444447 + 1.666666667x + x2 = -4.3055555553 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = -4.3055555553 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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