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Simplifying -5t2 + 9t + 21 = 0 Reorder the terms: 21 + 9t + -5t2 = 0 Solving 21 + 9t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.2 + -1.8t + t2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -1.8t + 4.2 + t2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -1.8t + t2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -1.8t + t2 = 0 + 4.2 -1.8t + t2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -1.8t + t2 = 4.2 The t term is -1.8t. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8t + 0.81 + t2 = 4.2 + 0.81 Reorder the terms: 0.81 + -1.8t + t2 = 4.2 + 0.81 Combine like terms: 4.2 + 0.81 = 5.01 0.81 + -1.8t + t2 = 5.01 Factor a perfect square on the left side: (t + -0.9)(t + -0.9) = 5.01 Calculate the square root of the right side: 2.238302929 Break this problem into two subproblems by setting (t + -0.9) equal to 2.238302929 and -2.238302929.Subproblem 1
t + -0.9 = 2.238302929 Simplifying t + -0.9 = 2.238302929 Reorder the terms: -0.9 + t = 2.238302929 Solving -0.9 + t = 2.238302929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + t = 2.238302929 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + t = 2.238302929 + 0.9 t = 2.238302929 + 0.9 Combine like terms: 2.238302929 + 0.9 = 3.138302929 t = 3.138302929 Simplifying t = 3.138302929Subproblem 2
t + -0.9 = -2.238302929 Simplifying t + -0.9 = -2.238302929 Reorder the terms: -0.9 + t = -2.238302929 Solving -0.9 + t = -2.238302929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + t = -2.238302929 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + t = -2.238302929 + 0.9 t = -2.238302929 + 0.9 Combine like terms: -2.238302929 + 0.9 = -1.338302929 t = -1.338302929 Simplifying t = -1.338302929Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.138302929, -1.338302929}
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