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Simplifying 7x2 + 56x = -94 Reorder the terms: 56x + 7x2 = -94 Solving 56x + 7x2 = -94 Solving for variable 'x'. Reorder the terms: 94 + 56x + 7x2 = -94 + 94 Combine like terms: -94 + 94 = 0 94 + 56x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 13.42857143 + 8x + x2 = 0 Move the constant term to the right: Add '-13.42857143' to each side of the equation. 13.42857143 + 8x + -13.42857143 + x2 = 0 + -13.42857143 Reorder the terms: 13.42857143 + -13.42857143 + 8x + x2 = 0 + -13.42857143 Combine like terms: 13.42857143 + -13.42857143 = 0.00000000 0.00000000 + 8x + x2 = 0 + -13.42857143 8x + x2 = 0 + -13.42857143 Combine like terms: 0 + -13.42857143 = -13.42857143 8x + x2 = -13.42857143 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -13.42857143 + 16 Reorder the terms: 16 + 8x + x2 = -13.42857143 + 16 Combine like terms: -13.42857143 + 16 = 2.57142857 16 + 8x + x2 = 2.57142857 Factor a perfect square on the left side: (x + 4)(x + 4) = 2.57142857 Calculate the square root of the right side: 1.603567451 Break this problem into two subproblems by setting (x + 4) equal to 1.603567451 and -1.603567451.Subproblem 1
x + 4 = 1.603567451 Simplifying x + 4 = 1.603567451 Reorder the terms: 4 + x = 1.603567451 Solving 4 + x = 1.603567451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 1.603567451 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.603567451 + -4 x = 1.603567451 + -4 Combine like terms: 1.603567451 + -4 = -2.396432549 x = -2.396432549 Simplifying x = -2.396432549Subproblem 2
x + 4 = -1.603567451 Simplifying x + 4 = -1.603567451 Reorder the terms: 4 + x = -1.603567451 Solving 4 + x = -1.603567451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -1.603567451 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.603567451 + -4 x = -1.603567451 + -4 Combine like terms: -1.603567451 + -4 = -5.603567451 x = -5.603567451 Simplifying x = -5.603567451Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.396432549, -5.603567451}
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