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Simplifying x2 + 15x + 52 = 0 Reorder the terms: 52 + 15x + x2 = 0 Solving 52 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + 15x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + 15x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + 15x + x2 = 0 + -52 15x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 15x + x2 = -52 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 = -52 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -52 + 56.25 Combine like terms: -52 + 56.25 = 4.25 56.25 + 15x + x2 = 4.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 7.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 7.5 = 2.061552813 Simplifying x + 7.5 = 2.061552813 Reorder the terms: 7.5 + x = 2.061552813 Solving 7.5 + x = 2.061552813 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 = 2.061552813 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 2.061552813 + -7.5 x = 2.061552813 + -7.5 Combine like terms: 2.061552813 + -7.5 = -5.438447187 x = -5.438447187 Simplifying x = -5.438447187Subproblem 2
x + 7.5 = -2.061552813 Simplifying x + 7.5 = -2.061552813 Reorder the terms: 7.5 + x = -2.061552813 Solving 7.5 + x = -2.061552813 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 = -2.061552813 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -2.061552813 + -7.5 x = -2.061552813 + -7.5 Combine like terms: -2.061552813 + -7.5 = -9.561552813 x = -9.561552813 Simplifying x = -9.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.438447187, -9.561552813}
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