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Simplifying a2 + -21a + 48 = 0 Reorder the terms: 48 + -21a + a2 = 0 Solving 48 + -21a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -21a + -48 + a2 = 0 + -48 Reorder the terms: 48 + -48 + -21a + a2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -21a + a2 = 0 + -48 -21a + a2 = 0 + -48 Combine like terms: 0 + -48 = -48 -21a + a2 = -48 The a term is -21a. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21a + 110.25 + a2 = -48 + 110.25 Reorder the terms: 110.25 + -21a + a2 = -48 + 110.25 Combine like terms: -48 + 110.25 = 62.25 110.25 + -21a + a2 = 62.25 Factor a perfect square on the left side: (a + -10.5)(a + -10.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (a + -10.5) equal to 7.889866919 and -7.889866919.Subproblem 1
a + -10.5 = 7.889866919 Simplifying a + -10.5 = 7.889866919 Reorder the terms: -10.5 + a = 7.889866919 Solving -10.5 + a = 7.889866919 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = 7.889866919 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = 7.889866919 + 10.5 a = 7.889866919 + 10.5 Combine like terms: 7.889866919 + 10.5 = 18.389866919 a = 18.389866919 Simplifying a = 18.389866919Subproblem 2
a + -10.5 = -7.889866919 Simplifying a + -10.5 = -7.889866919 Reorder the terms: -10.5 + a = -7.889866919 Solving -10.5 + a = -7.889866919 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = -7.889866919 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = -7.889866919 + 10.5 a = -7.889866919 + 10.5 Combine like terms: -7.889866919 + 10.5 = 2.610133081 a = 2.610133081 Simplifying a = 2.610133081Solution
The solution to the problem is based on the solutions from the subproblems. a = {18.389866919, 2.610133081}
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