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Simplifying 10x^{2}+ 12x + 18 = 0 Reorder the terms: 18 + 12x + 10x^{2}= 0 Solving 18 + 12x + 10x^{2}= 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 6x + 5x^{2}) = 0 Ignore the factor 2.## Subproblem 1

Set the factor '(9 + 6x + 5x^{2})' equal to zero and attempt to solve: Simplifying 9 + 6x + 5x^{2}= 0 Solving 9 + 6x + 5x^{2}= 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 1.2x + x^{2}= 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 1.2x + -1.8 + x^{2}= 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 1.2x + x^{2}= 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 1.2x + x^{2}= 0 + -1.8 1.2x + x^{2}= 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 1.2x + x^{2}= -1.8 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x^{2}= -1.8 + 0.36 Reorder the terms: 0.36 + 1.2x + x^{2}= -1.8 + 0.36 Combine like terms: -1.8 + 0.36 = -1.44 0.36 + 1.2x + x^{2}= -1.44 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = -1.44 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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