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Simplifying 9x + 7x + 5 + x2 = 0 Reorder the terms: 5 + 9x + 7x + x2 = 0 Combine like terms: 9x + 7x = 16x 5 + 16x + x2 = 0 Solving 5 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 16x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 16x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 16x + x2 = 0 + -5 16x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 16x + x2 = -5 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -5 + 64 Reorder the terms: 64 + 16x + x2 = -5 + 64 Combine like terms: -5 + 64 = 59 64 + 16x + x2 = 59 Factor a perfect square on the left side: (x + 8)(x + 8) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + 8) equal to 7.681145748 and -7.681145748.Subproblem 1
x + 8 = 7.681145748 Simplifying x + 8 = 7.681145748 Reorder the terms: 8 + x = 7.681145748 Solving 8 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 7.681145748 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.681145748 + -8 x = 7.681145748 + -8 Combine like terms: 7.681145748 + -8 = -0.318854252 x = -0.318854252 Simplifying x = -0.318854252Subproblem 2
x + 8 = -7.681145748 Simplifying x + 8 = -7.681145748 Reorder the terms: 8 + x = -7.681145748 Solving 8 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -7.681145748 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.681145748 + -8 x = -7.681145748 + -8 Combine like terms: -7.681145748 + -8 = -15.681145748 x = -15.681145748 Simplifying x = -15.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.318854252, -15.681145748}
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