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Simplifying (7x + 3)(7x + 3) = 18 Reorder the terms: (3 + 7x)(7x + 3) = 18 Reorder the terms: (3 + 7x)(3 + 7x) = 18 Multiply (3 + 7x) * (3 + 7x) (3(3 + 7x) + 7x * (3 + 7x)) = 18 ((3 * 3 + 7x * 3) + 7x * (3 + 7x)) = 18 ((9 + 21x) + 7x * (3 + 7x)) = 18 (9 + 21x + (3 * 7x + 7x * 7x)) = 18 (9 + 21x + (21x + 49x2)) = 18 Combine like terms: 21x + 21x = 42x (9 + 42x + 49x2) = 18 Solving 9 + 42x + 49x2 = 18 Solving for variable 'x'. Reorder the terms: 9 + -18 + 42x + 49x2 = 18 + -18 Combine like terms: 9 + -18 = -9 -9 + 42x + 49x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -9 + 42x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.1836734694 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.1836734694' to each side of the equation. -0.1836734694 + 0.8571428571x + 0.1836734694 + x2 = 0 + 0.1836734694 Reorder the terms: -0.1836734694 + 0.1836734694 + 0.8571428571x + x2 = 0 + 0.1836734694 Combine like terms: -0.1836734694 + 0.1836734694 = 0.0000000000 0.0000000000 + 0.8571428571x + x2 = 0 + 0.1836734694 0.8571428571x + x2 = 0 + 0.1836734694 Combine like terms: 0 + 0.1836734694 = 0.1836734694 0.8571428571x + x2 = 0.1836734694 The x term is 0.8571428571x. 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. 0.8571428571x + 0.1836734694 + x2 = 0.1836734694 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 0.1836734694 + 0.1836734694 Combine like terms: 0.1836734694 + 0.1836734694 = 0.3673469388 0.1836734694 + 0.8571428571x + x2 = 0.3673469388 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 0.3673469388 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 0.606091527 and -0.606091527.Subproblem 1
x + 0.4285714286 = 0.606091527 Simplifying x + 0.4285714286 = 0.606091527 Reorder the terms: 0.4285714286 + x = 0.606091527 Solving 0.4285714286 + x = 0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 0.606091527 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.606091527 + -0.4285714286 x = 0.606091527 + -0.4285714286 Combine like terms: 0.606091527 + -0.4285714286 = 0.1775200984 x = 0.1775200984 Simplifying x = 0.1775200984Subproblem 2
x + 0.4285714286 = -0.606091527 Simplifying x + 0.4285714286 = -0.606091527 Reorder the terms: 0.4285714286 + x = -0.606091527 Solving 0.4285714286 + x = -0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -0.606091527 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.606091527 + -0.4285714286 x = -0.606091527 + -0.4285714286 Combine like terms: -0.606091527 + -0.4285714286 = -1.0346629556 x = -1.0346629556 Simplifying x = -1.0346629556Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1775200984, -1.0346629556}
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