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Simplifying 5x + x2 = 1.96 Solving 5x + x2 = 1.96 Solving for variable 'x'. Reorder the terms: -1.96 + 5x + x2 = 1.96 + -1.96 Combine like terms: 1.96 + -1.96 = 0.00 -1.96 + 5x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '1.96' to each side of the equation. -1.96 + 5x + 1.96 + x2 = 0.00 + 1.96 Reorder the terms: -1.96 + 1.96 + 5x + x2 = 0.00 + 1.96 Combine like terms: -1.96 + 1.96 = 0.00 0.00 + 5x + x2 = 0.00 + 1.96 5x + x2 = 0.00 + 1.96 Combine like terms: 0.00 + 1.96 = 1.96 5x + x2 = 1.96 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 = 1.96 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1.96 + 6.25 Combine like terms: 1.96 + 6.25 = 8.21 6.25 + 5x + x2 = 8.21 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 8.21 Calculate the square root of the right side: 2.865309756 Break this problem into two subproblems by setting (x + 2.5) equal to 2.865309756 and -2.865309756.Subproblem 1
x + 2.5 = 2.865309756 Simplifying x + 2.5 = 2.865309756 Reorder the terms: 2.5 + x = 2.865309756 Solving 2.5 + x = 2.865309756 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 = 2.865309756 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.865309756 + -2.5 x = 2.865309756 + -2.5 Combine like terms: 2.865309756 + -2.5 = 0.365309756 x = 0.365309756 Simplifying x = 0.365309756Subproblem 2
x + 2.5 = -2.865309756 Simplifying x + 2.5 = -2.865309756 Reorder the terms: 2.5 + x = -2.865309756 Solving 2.5 + x = -2.865309756 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 = -2.865309756 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.865309756 + -2.5 x = -2.865309756 + -2.5 Combine like terms: -2.865309756 + -2.5 = -5.365309756 x = -5.365309756 Simplifying x = -5.365309756Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.365309756, -5.365309756}
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