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Simplifying 7a(3a + -4) = 12 Reorder the terms: 7a(-4 + 3a) = 12 (-4 * 7a + 3a * 7a) = 12 (-28a + 21a2) = 12 Solving -28a + 21a2 = 12 Solving for variable 'a'. Reorder the terms: -12 + -28a + 21a2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -28a + 21a2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.5714285714 + -1.333333333a + a2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -1.333333333a + 0.5714285714 + a2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -1.333333333a + a2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -1.333333333a + a2 = 0 + 0.5714285714 -1.333333333a + a2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -1.333333333a + a2 = 0.5714285714 The a term is -1.333333333a. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333a + 0.4444444442 + a2 = 0.5714285714 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333a + a2 = 0.5714285714 + 0.4444444442 Combine like terms: 0.5714285714 + 0.4444444442 = 1.0158730156 0.4444444442 + -1.333333333a + a2 = 1.0158730156 Factor a perfect square on the left side: (a + -0.6666666665)(a + -0.6666666665) = 1.0158730156 Calculate the square root of the right side: 1.007905261 Break this problem into two subproblems by setting (a + -0.6666666665) equal to 1.007905261 and -1.007905261.Subproblem 1
a + -0.6666666665 = 1.007905261 Simplifying a + -0.6666666665 = 1.007905261 Reorder the terms: -0.6666666665 + a = 1.007905261 Solving -0.6666666665 + a = 1.007905261 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + a = 1.007905261 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + a = 1.007905261 + 0.6666666665 a = 1.007905261 + 0.6666666665 Combine like terms: 1.007905261 + 0.6666666665 = 1.6745719275 a = 1.6745719275 Simplifying a = 1.6745719275Subproblem 2
a + -0.6666666665 = -1.007905261 Simplifying a + -0.6666666665 = -1.007905261 Reorder the terms: -0.6666666665 + a = -1.007905261 Solving -0.6666666665 + a = -1.007905261 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + a = -1.007905261 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + a = -1.007905261 + 0.6666666665 a = -1.007905261 + 0.6666666665 Combine like terms: -1.007905261 + 0.6666666665 = -0.3412385945 a = -0.3412385945 Simplifying a = -0.3412385945Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.6745719275, -0.3412385945}
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