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Simplifying (7x + -3)(7x + -3) = 7 Reorder the terms: (-3 + 7x)(7x + -3) = 7 Reorder the terms: (-3 + 7x)(-3 + 7x) = 7 Multiply (-3 + 7x) * (-3 + 7x) (-3(-3 + 7x) + 7x * (-3 + 7x)) = 7 ((-3 * -3 + 7x * -3) + 7x * (-3 + 7x)) = 7 ((9 + -21x) + 7x * (-3 + 7x)) = 7 (9 + -21x + (-3 * 7x + 7x * 7x)) = 7 (9 + -21x + (-21x + 49x2)) = 7 Combine like terms: -21x + -21x = -42x (9 + -42x + 49x2) = 7 Solving 9 + -42x + 49x2 = 7 Solving for variable 'x'. Reorder the terms: 9 + -7 + -42x + 49x2 = 7 + -7 Combine like terms: 9 + -7 = 2 2 + -42x + 49x2 = 7 + -7 Combine like terms: 7 + -7 = 0 2 + -42x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.04081632653 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '-0.04081632653' to each side of the equation. 0.04081632653 + -0.8571428571x + -0.04081632653 + x2 = 0 + -0.04081632653 Reorder the terms: 0.04081632653 + -0.04081632653 + -0.8571428571x + x2 = 0 + -0.04081632653 Combine like terms: 0.04081632653 + -0.04081632653 = 0.00000000000 0.00000000000 + -0.8571428571x + x2 = 0 + -0.04081632653 -0.8571428571x + x2 = 0 + -0.04081632653 Combine like terms: 0 + -0.04081632653 = -0.04081632653 -0.8571428571x + x2 = -0.04081632653 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 = -0.04081632653 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = -0.04081632653 + 0.1836734694 Combine like terms: -0.04081632653 + 0.1836734694 = 0.14285714287 0.1836734694 + -0.8571428571x + x2 = 0.14285714287 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.14285714287 Calculate the square root of the right side: 0.377964473 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.377964473 and -0.377964473.Subproblem 1
x + -0.4285714286 = 0.377964473 Simplifying x + -0.4285714286 = 0.377964473 Reorder the terms: -0.4285714286 + x = 0.377964473 Solving -0.4285714286 + x = 0.377964473 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 = 0.377964473 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.377964473 + 0.4285714286 x = 0.377964473 + 0.4285714286 Combine like terms: 0.377964473 + 0.4285714286 = 0.8065359016 x = 0.8065359016 Simplifying x = 0.8065359016Subproblem 2
x + -0.4285714286 = -0.377964473 Simplifying x + -0.4285714286 = -0.377964473 Reorder the terms: -0.4285714286 + x = -0.377964473 Solving -0.4285714286 + x = -0.377964473 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 = -0.377964473 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.377964473 + 0.4285714286 x = -0.377964473 + 0.4285714286 Combine like terms: -0.377964473 + 0.4285714286 = 0.0506069556 x = 0.0506069556 Simplifying x = 0.0506069556Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8065359016, 0.0506069556}
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