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Simplifying 7x(3x + 1) + -3 = 9 Reorder the terms: 7x(1 + 3x) + -3 = 9 (1 * 7x + 3x * 7x) + -3 = 9 (7x + 21x2) + -3 = 9 Reorder the terms: -3 + 7x + 21x2 = 9 Solving -3 + 7x + 21x2 = 9 Solving for variable 'x'. Reorder the terms: -3 + -9 + 7x + 21x2 = 9 + -9 Combine like terms: -3 + -9 = -12 -12 + 7x + 21x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -12 + 7x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.5714285714 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.3333333333x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.3333333333x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.5714285714 0.3333333333x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.3333333333x + x2 = 0.5714285714 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.5714285714 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.5714285714 + 0.02777777779 Combine like terms: 0.5714285714 + 0.02777777779 = 0.59920634919 0.02777777779 + 0.3333333333x + x2 = 0.59920634919 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.59920634919 Calculate the square root of the right side: 0.7740842 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.7740842 and -0.7740842.Subproblem 1
x + 0.1666666667 = 0.7740842 Simplifying x + 0.1666666667 = 0.7740842 Reorder the terms: 0.1666666667 + x = 0.7740842 Solving 0.1666666667 + x = 0.7740842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.7740842 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.7740842 + -0.1666666667 x = 0.7740842 + -0.1666666667 Combine like terms: 0.7740842 + -0.1666666667 = 0.6074175333 x = 0.6074175333 Simplifying x = 0.6074175333Subproblem 2
x + 0.1666666667 = -0.7740842 Simplifying x + 0.1666666667 = -0.7740842 Reorder the terms: 0.1666666667 + x = -0.7740842 Solving 0.1666666667 + x = -0.7740842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.7740842 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.7740842 + -0.1666666667 x = -0.7740842 + -0.1666666667 Combine like terms: -0.7740842 + -0.1666666667 = -0.9407508667 x = -0.9407508667 Simplifying x = -0.9407508667Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6074175333, -0.9407508667}
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