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Simplifying 448(t) = -16t * -16t + 16t + 480 Reorder the terms for easier multiplication: 448t = -16 * -16t * t + 16t + 480 Multiply -16 * -16 448t = 256t * t + 16t + 480 Multiply t * t 448t = 256t2 + 16t + 480 Reorder the terms: 448t = 480 + 16t + 256t2 Solving 448t = 480 + 16t + 256t2 Solving for variable 't'. Reorder the terms: -480 + 448t + -16t + -256t2 = 480 + 16t + 256t2 + -480 + -16t + -256t2 Combine like terms: 448t + -16t = 432t -480 + 432t + -256t2 = 480 + 16t + 256t2 + -480 + -16t + -256t2 Reorder the terms: -480 + 432t + -256t2 = 480 + -480 + 16t + -16t + 256t2 + -256t2 Combine like terms: 480 + -480 = 0 -480 + 432t + -256t2 = 0 + 16t + -16t + 256t2 + -256t2 -480 + 432t + -256t2 = 16t + -16t + 256t2 + -256t2 Combine like terms: 16t + -16t = 0 -480 + 432t + -256t2 = 0 + 256t2 + -256t2 -480 + 432t + -256t2 = 256t2 + -256t2 Combine like terms: 256t2 + -256t2 = 0 -480 + 432t + -256t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-30 + 27t + -16t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-30 + 27t + -16t2)' equal to zero and attempt to solve: Simplifying -30 + 27t + -16t2 = 0 Solving -30 + 27t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.875 + -1.6875t + t2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -1.6875t + -1.875 + t2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -1.6875t + t2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -1.6875t + t2 = 0 + -1.875 -1.6875t + t2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -1.6875t + t2 = -1.875 The t term is -1.6875t. Take half its coefficient (-0.84375). Square it (0.7119140625) and add it to both sides. Add '0.7119140625' to each side of the equation. -1.6875t + 0.7119140625 + t2 = -1.875 + 0.7119140625 Reorder the terms: 0.7119140625 + -1.6875t + t2 = -1.875 + 0.7119140625 Combine like terms: -1.875 + 0.7119140625 = -1.1630859375 0.7119140625 + -1.6875t + t2 = -1.1630859375 Factor a perfect square on the left side: (t + -0.84375)(t + -0.84375) = -1.1630859375 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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