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Simplifying x2 + -14x + -25.5 = 0 Reorder the terms: -25.5 + -14x + x2 = 0 Solving -25.5 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + -14x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + -14x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + -14x + x2 = 0 + 25.5 -14x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 -14x + x2 = 25.5 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 25.5 + 49 Reorder the terms: 49 + -14x + x2 = 25.5 + 49 Combine like terms: 25.5 + 49 = 74.5 49 + -14x + x2 = 74.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 74.5 Calculate the square root of the right side: 8.631338251 Break this problem into two subproblems by setting (x + -7) equal to 8.631338251 and -8.631338251.Subproblem 1
x + -7 = 8.631338251 Simplifying x + -7 = 8.631338251 Reorder the terms: -7 + x = 8.631338251 Solving -7 + x = 8.631338251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 8.631338251 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.631338251 + 7 x = 8.631338251 + 7 Combine like terms: 8.631338251 + 7 = 15.631338251 x = 15.631338251 Simplifying x = 15.631338251Subproblem 2
x + -7 = -8.631338251 Simplifying x + -7 = -8.631338251 Reorder the terms: -7 + x = -8.631338251 Solving -7 + x = -8.631338251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -8.631338251 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.631338251 + 7 x = -8.631338251 + 7 Combine like terms: -8.631338251 + 7 = -1.631338251 x = -1.631338251 Simplifying x = -1.631338251Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.631338251, -1.631338251}
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