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Simplifying x2 + -5x + 0.96 = 0 Reorder the terms: 0.96 + -5x + x2 = 0 Solving 0.96 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.96' to each side of the equation. 0.96 + -5x + -0.96 + x2 = 0 + -0.96 Reorder the terms: 0.96 + -0.96 + -5x + x2 = 0 + -0.96 Combine like terms: 0.96 + -0.96 = 0.00 0.00 + -5x + x2 = 0 + -0.96 -5x + x2 = 0 + -0.96 Combine like terms: 0 + -0.96 = -0.96 -5x + x2 = -0.96 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.96 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.96 + 6.25 Combine like terms: -0.96 + 6.25 = 5.29 6.25 + -5x + x2 = 5.29 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.29 Calculate the square root of the right side: 2.3 Break this problem into two subproblems by setting (x + -2.5) equal to 2.3 and -2.3.Subproblem 1
x + -2.5 = 2.3 Simplifying x + -2.5 = 2.3 Reorder the terms: -2.5 + x = 2.3 Solving -2.5 + x = 2.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.3 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.3 + 2.5 x = 2.3 + 2.5 Combine like terms: 2.3 + 2.5 = 4.8 x = 4.8 Simplifying x = 4.8Subproblem 2
x + -2.5 = -2.3 Simplifying x + -2.5 = -2.3 Reorder the terms: -2.5 + x = -2.3 Solving -2.5 + x = -2.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.3 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.3 + 2.5 x = -2.3 + 2.5 Combine like terms: -2.3 + 2.5 = 0.2 x = 0.2 Simplifying x = 0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8, 0.2}
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