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Simplifying -7a2 = -6a + -18 Reorder the terms: -7a2 = -18 + -6a Solving -7a2 = -18 + -6a Solving for variable 'a'. Reorder the terms: 18 + 6a + -7a2 = -18 + -6a + 18 + 6a Reorder the terms: 18 + 6a + -7a2 = -18 + 18 + -6a + 6a Combine like terms: -18 + 18 = 0 18 + 6a + -7a2 = 0 + -6a + 6a 18 + 6a + -7a2 = -6a + 6a Combine like terms: -6a + 6a = 0 18 + 6a + -7a2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2.571428571 + -0.8571428571a + a2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -0.8571428571a + 2.571428571 + a2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -0.8571428571a + a2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -0.8571428571a + a2 = 0 + 2.571428571 -0.8571428571a + a2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -0.8571428571a + a2 = 2.571428571 The a term is -0.8571428571a. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571a + 0.1836734694 + a2 = 2.571428571 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571a + a2 = 2.571428571 + 0.1836734694 Combine like terms: 2.571428571 + 0.1836734694 = 2.7551020404 0.1836734694 + -0.8571428571a + a2 = 2.7551020404 Factor a perfect square on the left side: (a + -0.4285714286)(a + -0.4285714286) = 2.7551020404 Calculate the square root of the right side: 1.659850005 Break this problem into two subproblems by setting (a + -0.4285714286) equal to 1.659850005 and -1.659850005.Subproblem 1
a + -0.4285714286 = 1.659850005 Simplifying a + -0.4285714286 = 1.659850005 Reorder the terms: -0.4285714286 + a = 1.659850005 Solving -0.4285714286 + a = 1.659850005 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + a = 1.659850005 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + a = 1.659850005 + 0.4285714286 a = 1.659850005 + 0.4285714286 Combine like terms: 1.659850005 + 0.4285714286 = 2.0884214336 a = 2.0884214336 Simplifying a = 2.0884214336Subproblem 2
a + -0.4285714286 = -1.659850005 Simplifying a + -0.4285714286 = -1.659850005 Reorder the terms: -0.4285714286 + a = -1.659850005 Solving -0.4285714286 + a = -1.659850005 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + a = -1.659850005 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + a = -1.659850005 + 0.4285714286 a = -1.659850005 + 0.4285714286 Combine like terms: -1.659850005 + 0.4285714286 = -1.2312785764 a = -1.2312785764 Simplifying a = -1.2312785764Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.0884214336, -1.2312785764}
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