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Simplifying 7x(x + 9) = -8 Reorder the terms: 7x(9 + x) = -8 (9 * 7x + x * 7x) = -8 (63x + 7x2) = -8 Solving 63x + 7x2 = -8 Solving for variable 'x'. Reorder the terms: 8 + 63x + 7x2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 63x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.142857143 + 9x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + 9x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + 9x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + 9x + x2 = 0 + -1.142857143 9x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 9x + x2 = -1.142857143 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -1.142857143 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -1.142857143 + 20.25 Combine like terms: -1.142857143 + 20.25 = 19.107142857 20.25 + 9x + x2 = 19.107142857 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 19.107142857 Calculate the square root of the right side: 4.371171794 Break this problem into two subproblems by setting (x + 4.5) equal to 4.371171794 and -4.371171794.Subproblem 1
x + 4.5 = 4.371171794 Simplifying x + 4.5 = 4.371171794 Reorder the terms: 4.5 + x = 4.371171794 Solving 4.5 + x = 4.371171794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.371171794 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.371171794 + -4.5 x = 4.371171794 + -4.5 Combine like terms: 4.371171794 + -4.5 = -0.128828206 x = -0.128828206 Simplifying x = -0.128828206Subproblem 2
x + 4.5 = -4.371171794 Simplifying x + 4.5 = -4.371171794 Reorder the terms: 4.5 + x = -4.371171794 Solving 4.5 + x = -4.371171794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.371171794 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.371171794 + -4.5 x = -4.371171794 + -4.5 Combine like terms: -4.371171794 + -4.5 = -8.871171794 x = -8.871171794 Simplifying x = -8.871171794Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.128828206, -8.871171794}
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