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Simplifying x2 + -15.5x + -45 = 0 Reorder the terms: -45 + -15.5x + x2 = 0 Solving -45 + -15.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -15.5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -15.5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -15.5x + x2 = 0 + 45 -15.5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -15.5x + x2 = 45 The x term is -15.5x. Take half its coefficient (-7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. -15.5x + 60.0625 + x2 = 45 + 60.0625 Reorder the terms: 60.0625 + -15.5x + x2 = 45 + 60.0625 Combine like terms: 45 + 60.0625 = 105.0625 60.0625 + -15.5x + x2 = 105.0625 Factor a perfect square on the left side: (x + -7.75)(x + -7.75) = 105.0625 Calculate the square root of the right side: 10.25 Break this problem into two subproblems by setting (x + -7.75) equal to 10.25 and -10.25.Subproblem 1
x + -7.75 = 10.25 Simplifying x + -7.75 = 10.25 Reorder the terms: -7.75 + x = 10.25 Solving -7.75 + x = 10.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = 10.25 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = 10.25 + 7.75 x = 10.25 + 7.75 Combine like terms: 10.25 + 7.75 = 18 x = 18 Simplifying x = 18Subproblem 2
x + -7.75 = -10.25 Simplifying x + -7.75 = -10.25 Reorder the terms: -7.75 + x = -10.25 Solving -7.75 + x = -10.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = -10.25 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = -10.25 + 7.75 x = -10.25 + 7.75 Combine like terms: -10.25 + 7.75 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {18, -2.5}
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