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Simplifying x2 + 15x + 7 = 0 Reorder the terms: 7 + 15x + x2 = 0 Solving 7 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 15x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 15x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 15x + x2 = 0 + -7 15x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 15x + x2 = -7 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -7 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -7 + 56.25 Combine like terms: -7 + 56.25 = 49.25 56.25 + 15x + x2 = 49.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + 7.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + 7.5 = 7.017834424 Simplifying x + 7.5 = 7.017834424 Reorder the terms: 7.5 + x = 7.017834424 Solving 7.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 7.017834424 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.017834424 + -7.5 x = 7.017834424 + -7.5 Combine like terms: 7.017834424 + -7.5 = -0.482165576 x = -0.482165576 Simplifying x = -0.482165576Subproblem 2
x + 7.5 = -7.017834424 Simplifying x + 7.5 = -7.017834424 Reorder the terms: 7.5 + x = -7.017834424 Solving 7.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -7.017834424 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.017834424 + -7.5 x = -7.017834424 + -7.5 Combine like terms: -7.017834424 + -7.5 = -14.517834424 x = -14.517834424 Simplifying x = -14.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.482165576, -14.517834424}
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