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Simplifying 45x2 + 20x + 15 = 0 Reorder the terms: 15 + 20x + 45x2 = 0 Solving 15 + 20x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + 4x + 9x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + 4x + 9x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + 9x2 = 0 Solving 3 + 4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3333333333 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.4444444444x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.4444444444x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.4444444444x + x2 = 0 + -0.3333333333 0.4444444444x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.4444444444x + x2 = -0.3333333333 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = -0.3333333333 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = -0.3333333333 + 0.04938271604 Combine like terms: -0.3333333333 + 0.04938271604 = -0.28395061726 0.04938271604 + 0.4444444444x + x2 = -0.28395061726 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = -0.28395061726 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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