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Simplifying 7x2 = -47x + 30 Reorder the terms: 7x2 = 30 + -47x Solving 7x2 = 30 + -47x Solving for variable 'x'. Reorder the terms: -30 + 47x + 7x2 = 30 + -47x + -30 + 47x Reorder the terms: -30 + 47x + 7x2 = 30 + -30 + -47x + 47x Combine like terms: 30 + -30 = 0 -30 + 47x + 7x2 = 0 + -47x + 47x -30 + 47x + 7x2 = -47x + 47x Combine like terms: -47x + 47x = 0 -30 + 47x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.285714286 + 6.714285714x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + 6.714285714x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + 6.714285714x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + 6.714285714x + x2 = 0 + 4.285714286 6.714285714x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 6.714285714x + x2 = 4.285714286 The x term is 6.714285714x. Take half its coefficient (3.357142857). Square it (11.27040816) and add it to both sides. Add '11.27040816' to each side of the equation. 6.714285714x + 11.27040816 + x2 = 4.285714286 + 11.27040816 Reorder the terms: 11.27040816 + 6.714285714x + x2 = 4.285714286 + 11.27040816 Combine like terms: 4.285714286 + 11.27040816 = 15.556122446 11.27040816 + 6.714285714x + x2 = 15.556122446 Factor a perfect square on the left side: (x + 3.357142857)(x + 3.357142857) = 15.556122446 Calculate the square root of the right side: 3.944125055 Break this problem into two subproblems by setting (x + 3.357142857) equal to 3.944125055 and -3.944125055.Subproblem 1
x + 3.357142857 = 3.944125055 Simplifying x + 3.357142857 = 3.944125055 Reorder the terms: 3.357142857 + x = 3.944125055 Solving 3.357142857 + x = 3.944125055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.357142857' to each side of the equation. 3.357142857 + -3.357142857 + x = 3.944125055 + -3.357142857 Combine like terms: 3.357142857 + -3.357142857 = 0.000000000 0.000000000 + x = 3.944125055 + -3.357142857 x = 3.944125055 + -3.357142857 Combine like terms: 3.944125055 + -3.357142857 = 0.586982198 x = 0.586982198 Simplifying x = 0.586982198Subproblem 2
x + 3.357142857 = -3.944125055 Simplifying x + 3.357142857 = -3.944125055 Reorder the terms: 3.357142857 + x = -3.944125055 Solving 3.357142857 + x = -3.944125055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.357142857' to each side of the equation. 3.357142857 + -3.357142857 + x = -3.944125055 + -3.357142857 Combine like terms: 3.357142857 + -3.357142857 = 0.000000000 0.000000000 + x = -3.944125055 + -3.357142857 x = -3.944125055 + -3.357142857 Combine like terms: -3.944125055 + -3.357142857 = -7.301267912 x = -7.301267912 Simplifying x = -7.301267912Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.586982198, -7.301267912}
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