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Simplifying x2 + 9.5x + -5 = 0 Reorder the terms: -5 + 9.5x + x2 = 0 Solving -5 + 9.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 9.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 9.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 9.5x + x2 = 0 + 5 9.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 9.5x + x2 = 5 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 5 + 22.5625 Combine like terms: 5 + 22.5625 = 27.5625 22.5625 + 9.5x + x2 = 27.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 27.5625 Calculate the square root of the right side: 5.25 Break this problem into two subproblems by setting (x + 4.75) equal to 5.25 and -5.25.Subproblem 1
x + 4.75 = 5.25 Simplifying x + 4.75 = 5.25 Reorder the terms: 4.75 + x = 5.25 Solving 4.75 + x = 5.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 5.25 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 5.25 + -4.75 x = 5.25 + -4.75 Combine like terms: 5.25 + -4.75 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 4.75 = -5.25 Simplifying x + 4.75 = -5.25 Reorder the terms: 4.75 + x = -5.25 Solving 4.75 + x = -5.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -5.25 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -5.25 + -4.75 x = -5.25 + -4.75 Combine like terms: -5.25 + -4.75 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -10}
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