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Simplifying 100r2 + 200r + 144 = 0 Reorder the terms: 144 + 200r + 100r2 = 0 Solving 144 + 200r + 100r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(36 + 50r + 25r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(36 + 50r + 25r2)' equal to zero and attempt to solve: Simplifying 36 + 50r + 25r2 = 0 Solving 36 + 50r + 25r2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.44 + 2r + r2 = 0 Move the constant term to the right: Add '-1.44' to each side of the equation. 1.44 + 2r + -1.44 + r2 = 0 + -1.44 Reorder the terms: 1.44 + -1.44 + 2r + r2 = 0 + -1.44 Combine like terms: 1.44 + -1.44 = 0.00 0.00 + 2r + r2 = 0 + -1.44 2r + r2 = 0 + -1.44 Combine like terms: 0 + -1.44 = -1.44 2r + r2 = -1.44 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = -1.44 + 1 Reorder the terms: 1 + 2r + r2 = -1.44 + 1 Combine like terms: -1.44 + 1 = -0.44 1 + 2r + r2 = -0.44 Factor a perfect square on the left side: (r + 1)(r + 1) = -0.44 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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