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Simplifying 5t2 + -15t + 290 = 0 Reorder the terms: 290 + -15t + 5t2 = 0 Solving 290 + -15t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(58 + -3t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(58 + -3t + t2)' equal to zero and attempt to solve: Simplifying 58 + -3t + t2 = 0 Solving 58 + -3t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + -3t + -58 + t2 = 0 + -58 Reorder the terms: 58 + -58 + -3t + t2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + -3t + t2 = 0 + -58 -3t + t2 = 0 + -58 Combine like terms: 0 + -58 = -58 -3t + t2 = -58 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = -58 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -58 + 2.25 Combine like terms: -58 + 2.25 = -55.75 2.25 + -3t + t2 = -55.75 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = -55.75 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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