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Simplifying x2 + -4.86x + 2.69 = 0 Reorder the terms: 2.69 + -4.86x + x2 = 0 Solving 2.69 + -4.86x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2.69' to each side of the equation. 2.69 + -4.86x + -2.69 + x2 = 0 + -2.69 Reorder the terms: 2.69 + -2.69 + -4.86x + x2 = 0 + -2.69 Combine like terms: 2.69 + -2.69 = 0.00 0.00 + -4.86x + x2 = 0 + -2.69 -4.86x + x2 = 0 + -2.69 Combine like terms: 0 + -2.69 = -2.69 -4.86x + x2 = -2.69 The x term is -4.86x. Take half its coefficient (-2.43). Square it (5.9049) and add it to both sides. Add '5.9049' to each side of the equation. -4.86x + 5.9049 + x2 = -2.69 + 5.9049 Reorder the terms: 5.9049 + -4.86x + x2 = -2.69 + 5.9049 Combine like terms: -2.69 + 5.9049 = 3.2149 5.9049 + -4.86x + x2 = 3.2149 Factor a perfect square on the left side: (x + -2.43)(x + -2.43) = 3.2149 Calculate the square root of the right side: 1.793014222 Break this problem into two subproblems by setting (x + -2.43) equal to 1.793014222 and -1.793014222.Subproblem 1
x + -2.43 = 1.793014222 Simplifying x + -2.43 = 1.793014222 Reorder the terms: -2.43 + x = 1.793014222 Solving -2.43 + x = 1.793014222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.43' to each side of the equation. -2.43 + 2.43 + x = 1.793014222 + 2.43 Combine like terms: -2.43 + 2.43 = 0.00 0.00 + x = 1.793014222 + 2.43 x = 1.793014222 + 2.43 Combine like terms: 1.793014222 + 2.43 = 4.223014222 x = 4.223014222 Simplifying x = 4.223014222Subproblem 2
x + -2.43 = -1.793014222 Simplifying x + -2.43 = -1.793014222 Reorder the terms: -2.43 + x = -1.793014222 Solving -2.43 + x = -1.793014222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.43' to each side of the equation. -2.43 + 2.43 + x = -1.793014222 + 2.43 Combine like terms: -2.43 + 2.43 = 0.00 0.00 + x = -1.793014222 + 2.43 x = -1.793014222 + 2.43 Combine like terms: -1.793014222 + 2.43 = 0.636985778 x = 0.636985778 Simplifying x = 0.636985778Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.223014222, 0.636985778}
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