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Simplifying 0 = 25a2 + -20a + -4 Reorder the terms: 0 = -4 + -20a + 25a2 Solving 0 = -4 + -20a + 25a2 Solving for variable 'a'. Combine like terms: 0 + 4 = 4 4 + 20a + -25a2 = -4 + -20a + 25a2 + 4 + 20a + -25a2 Reorder the terms: 4 + 20a + -25a2 = -4 + 4 + -20a + 20a + 25a2 + -25a2 Combine like terms: -4 + 4 = 0 4 + 20a + -25a2 = 0 + -20a + 20a + 25a2 + -25a2 4 + 20a + -25a2 = -20a + 20a + 25a2 + -25a2 Combine like terms: -20a + 20a = 0 4 + 20a + -25a2 = 0 + 25a2 + -25a2 4 + 20a + -25a2 = 25a2 + -25a2 Combine like terms: 25a2 + -25a2 = 0 4 + 20a + -25a2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.16 + -0.8a + a2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -0.8a + 0.16 + a2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -0.8a + a2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -0.8a + a2 = 0 + 0.16 -0.8a + a2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -0.8a + a2 = 0.16 The a term is -0.8a. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8a + 0.16 + a2 = 0.16 + 0.16 Reorder the terms: 0.16 + -0.8a + a2 = 0.16 + 0.16 Combine like terms: 0.16 + 0.16 = 0.32 0.16 + -0.8a + a2 = 0.32 Factor a perfect square on the left side: (a + -0.4)(a + -0.4) = 0.32 Calculate the square root of the right side: 0.565685425 Break this problem into two subproblems by setting (a + -0.4) equal to 0.565685425 and -0.565685425.Subproblem 1
a + -0.4 = 0.565685425 Simplifying a + -0.4 = 0.565685425 Reorder the terms: -0.4 + a = 0.565685425 Solving -0.4 + a = 0.565685425 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + a = 0.565685425 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + a = 0.565685425 + 0.4 a = 0.565685425 + 0.4 Combine like terms: 0.565685425 + 0.4 = 0.965685425 a = 0.965685425 Simplifying a = 0.965685425Subproblem 2
a + -0.4 = -0.565685425 Simplifying a + -0.4 = -0.565685425 Reorder the terms: -0.4 + a = -0.565685425 Solving -0.4 + a = -0.565685425 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + a = -0.565685425 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + a = -0.565685425 + 0.4 a = -0.565685425 + 0.4 Combine like terms: -0.565685425 + 0.4 = -0.165685425 a = -0.165685425 Simplifying a = -0.165685425Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.965685425, -0.165685425}
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