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Simplifying x2 + -14x + -161.25 = 0 Reorder the terms: -161.25 + -14x + x2 = 0 Solving -161.25 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '161.25' to each side of the equation. -161.25 + -14x + 161.25 + x2 = 0 + 161.25 Reorder the terms: -161.25 + 161.25 + -14x + x2 = 0 + 161.25 Combine like terms: -161.25 + 161.25 = 0.00 0.00 + -14x + x2 = 0 + 161.25 -14x + x2 = 0 + 161.25 Combine like terms: 0 + 161.25 = 161.25 -14x + x2 = 161.25 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 = 161.25 + 49 Reorder the terms: 49 + -14x + x2 = 161.25 + 49 Combine like terms: 161.25 + 49 = 210.25 49 + -14x + x2 = 210.25 Factor a perfect square on the left side: (x + -7)(x + -7) = 210.25 Calculate the square root of the right side: 14.5 Break this problem into two subproblems by setting (x + -7) equal to 14.5 and -14.5.Subproblem 1
x + -7 = 14.5 Simplifying x + -7 = 14.5 Reorder the terms: -7 + x = 14.5 Solving -7 + x = 14.5 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 = 14.5 + 7 Combine like terms: -7 + 7 = 0 0 + x = 14.5 + 7 x = 14.5 + 7 Combine like terms: 14.5 + 7 = 21.5 x = 21.5 Simplifying x = 21.5Subproblem 2
x + -7 = -14.5 Simplifying x + -7 = -14.5 Reorder the terms: -7 + x = -14.5 Solving -7 + x = -14.5 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 = -14.5 + 7 Combine like terms: -7 + 7 = 0 0 + x = -14.5 + 7 x = -14.5 + 7 Combine like terms: -14.5 + 7 = -7.5 x = -7.5 Simplifying x = -7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.5, -7.5}
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