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Simplifying -3t2 + 42t + 23 = 0 Reorder the terms: 23 + 42t + -3t2 = 0 Solving 23 + 42t + -3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -7.666666667 + -14t + t2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + -14t + 7.666666667 + t2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + -14t + t2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + -14t + t2 = 0 + 7.666666667 -14t + t2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 -14t + t2 = 7.666666667 The t term is -14t. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14t + 49 + t2 = 7.666666667 + 49 Reorder the terms: 49 + -14t + t2 = 7.666666667 + 49 Combine like terms: 7.666666667 + 49 = 56.666666667 49 + -14t + t2 = 56.666666667 Factor a perfect square on the left side: (t + -7)(t + -7) = 56.666666667 Calculate the square root of the right side: 7.527726527 Break this problem into two subproblems by setting (t + -7) equal to 7.527726527 and -7.527726527.Subproblem 1
t + -7 = 7.527726527 Simplifying t + -7 = 7.527726527 Reorder the terms: -7 + t = 7.527726527 Solving -7 + t = 7.527726527 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 7.527726527 + 7 Combine like terms: -7 + 7 = 0 0 + t = 7.527726527 + 7 t = 7.527726527 + 7 Combine like terms: 7.527726527 + 7 = 14.527726527 t = 14.527726527 Simplifying t = 14.527726527Subproblem 2
t + -7 = -7.527726527 Simplifying t + -7 = -7.527726527 Reorder the terms: -7 + t = -7.527726527 Solving -7 + t = -7.527726527 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = -7.527726527 + 7 Combine like terms: -7 + 7 = 0 0 + t = -7.527726527 + 7 t = -7.527726527 + 7 Combine like terms: -7.527726527 + 7 = -0.527726527 t = -0.527726527 Simplifying t = -0.527726527Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.527726527, -0.527726527}
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