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Simplifying 7x2 + 47x + 7 = 0 Reorder the terms: 7 + 47x + 7x2 = 0 Solving 7 + 47x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + 6.714285714x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 6.714285714x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 6.714285714x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6.714285714x + x2 = 0 + -1 6.714285714x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 6.714285714x + x2 = -1 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 = -1 + 11.27040816 Reorder the terms: 11.27040816 + 6.714285714x + x2 = -1 + 11.27040816 Combine like terms: -1 + 11.27040816 = 10.27040816 11.27040816 + 6.714285714x + x2 = 10.27040816 Factor a perfect square on the left side: (x + 3.357142857)(x + 3.357142857) = 10.27040816 Calculate the square root of the right side: 3.204747753 Break this problem into two subproblems by setting (x + 3.357142857) equal to 3.204747753 and -3.204747753.Subproblem 1
x + 3.357142857 = 3.204747753 Simplifying x + 3.357142857 = 3.204747753 Reorder the terms: 3.357142857 + x = 3.204747753 Solving 3.357142857 + x = 3.204747753 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 = 3.204747753 + -3.357142857 Combine like terms: 3.357142857 + -3.357142857 = 0.000000000 0.000000000 + x = 3.204747753 + -3.357142857 x = 3.204747753 + -3.357142857 Combine like terms: 3.204747753 + -3.357142857 = -0.152395104 x = -0.152395104 Simplifying x = -0.152395104Subproblem 2
x + 3.357142857 = -3.204747753 Simplifying x + 3.357142857 = -3.204747753 Reorder the terms: 3.357142857 + x = -3.204747753 Solving 3.357142857 + x = -3.204747753 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 = -3.204747753 + -3.357142857 Combine like terms: 3.357142857 + -3.357142857 = 0.000000000 0.000000000 + x = -3.204747753 + -3.357142857 x = -3.204747753 + -3.357142857 Combine like terms: -3.204747753 + -3.357142857 = -6.56189061 x = -6.56189061 Simplifying x = -6.56189061Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.152395104, -6.56189061}
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