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Simplifying 7a2 + -4 = -14a Reorder the terms: -4 + 7a2 = -14a Solving -4 + 7a2 = -14a Solving for variable 'a'. Reorder the terms: -4 + 14a + 7a2 = -14a + 14a Combine like terms: -14a + 14a = 0 -4 + 14a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 2a + a2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 2a + 0.5714285714 + a2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 2a + a2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 2a + a2 = 0 + 0.5714285714 2a + a2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 2a + a2 = 0.5714285714 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 0.5714285714 + 1 Reorder the terms: 1 + 2a + a2 = 0.5714285714 + 1 Combine like terms: 0.5714285714 + 1 = 1.5714285714 1 + 2a + a2 = 1.5714285714 Factor a perfect square on the left side: (a + 1)(a + 1) = 1.5714285714 Calculate the square root of the right side: 1.253566341 Break this problem into two subproblems by setting (a + 1) equal to 1.253566341 and -1.253566341.Subproblem 1
a + 1 = 1.253566341 Simplifying a + 1 = 1.253566341 Reorder the terms: 1 + a = 1.253566341 Solving 1 + a = 1.253566341 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 1.253566341 + -1 Combine like terms: 1 + -1 = 0 0 + a = 1.253566341 + -1 a = 1.253566341 + -1 Combine like terms: 1.253566341 + -1 = 0.253566341 a = 0.253566341 Simplifying a = 0.253566341Subproblem 2
a + 1 = -1.253566341 Simplifying a + 1 = -1.253566341 Reorder the terms: 1 + a = -1.253566341 Solving 1 + a = -1.253566341 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -1.253566341 + -1 Combine like terms: 1 + -1 = 0 0 + a = -1.253566341 + -1 a = -1.253566341 + -1 Combine like terms: -1.253566341 + -1 = -2.253566341 a = -2.253566341 Simplifying a = -2.253566341Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.253566341, -2.253566341}
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