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Simplifying 21 = t2 + -1t Reorder the terms: 21 = -1t + t2 Solving 21 = -1t + t2 Solving for variable 't'. Reorder the terms: 21 + t + -1t2 = -1t + t + t2 + -1t2 Combine like terms: -1t + t = 0 21 + t + -1t2 = 0 + t2 + -1t2 21 + t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 21 + t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -1t + t2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -1t + 21 + t2 = 0 + 21 Reorder the terms: -21 + 21 + -1t + t2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1t + t2 = 0 + 21 -1t + t2 = 0 + 21 Combine like terms: 0 + 21 = 21 -1t + t2 = 21 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 21 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 21 + 0.25 Combine like terms: 21 + 0.25 = 21.25 0.25 + -1t + t2 = 21.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (t + 0.5) equal to 4.609772229 and -4.609772229.Subproblem 1
t + 0.5 = 4.609772229 Simplifying t + 0.5 = 4.609772229 Reorder the terms: 0.5 + t = 4.609772229 Solving 0.5 + t = 4.609772229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 4.609772229 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 4.609772229 + -0.5 t = 4.609772229 + -0.5 Combine like terms: 4.609772229 + -0.5 = 4.109772229 t = 4.109772229 Simplifying t = 4.109772229Subproblem 2
t + 0.5 = -4.609772229 Simplifying t + 0.5 = -4.609772229 Reorder the terms: 0.5 + t = -4.609772229 Solving 0.5 + t = -4.609772229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -4.609772229 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -4.609772229 + -0.5 t = -4.609772229 + -0.5 Combine like terms: -4.609772229 + -0.5 = -5.109772229 t = -5.109772229 Simplifying t = -5.109772229Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.109772229, -5.109772229}
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