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Simplifying -1.5t2 + 36t + 6 = 0 Reorder the terms: 6 + 36t + -1.5t2 = 0 Solving 6 + 36t + -1.5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -4 + -24t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -24t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -24t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -24t + t2 = 0 + 4 -24t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -24t + t2 = 4 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = 4 + 144 Reorder the terms: 144 + -24t + t2 = 4 + 144 Combine like terms: 4 + 144 = 148 144 + -24t + t2 = 148 Factor a perfect square on the left side: (t + -12)(t + -12) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (t + -12) equal to 12.165525061 and -12.165525061.Subproblem 1
t + -12 = 12.165525061 Simplifying t + -12 = 12.165525061 Reorder the terms: -12 + t = 12.165525061 Solving -12 + t = 12.165525061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 12.165525061 + 12 Combine like terms: -12 + 12 = 0 0 + t = 12.165525061 + 12 t = 12.165525061 + 12 Combine like terms: 12.165525061 + 12 = 24.165525061 t = 24.165525061 Simplifying t = 24.165525061Subproblem 2
t + -12 = -12.165525061 Simplifying t + -12 = -12.165525061 Reorder the terms: -12 + t = -12.165525061 Solving -12 + t = -12.165525061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -12.165525061 + 12 Combine like terms: -12 + 12 = 0 0 + t = -12.165525061 + 12 t = -12.165525061 + 12 Combine like terms: -12.165525061 + 12 = -0.165525061 t = -0.165525061 Simplifying t = -0.165525061Solution
The solution to the problem is based on the solutions from the subproblems. t = {24.165525061, -0.165525061}
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