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Simplifying x2 + 12.42x + x = 3 Reorder the terms: 12.42x + x + x2 = 3 Combine like terms: 12.42x + x = 13.42x 13.42x + x2 = 3 Solving 13.42x + x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 13.42x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 13.42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 13.42x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 13.42x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 13.42x + x2 = 0 + 3 13.42x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 13.42x + x2 = 3 The x term is 13.42x. Take half its coefficient (6.71). Square it (45.0241) and add it to both sides. Add '45.0241' to each side of the equation. 13.42x + 45.0241 + x2 = 3 + 45.0241 Reorder the terms: 45.0241 + 13.42x + x2 = 3 + 45.0241 Combine like terms: 3 + 45.0241 = 48.0241 45.0241 + 13.42x + x2 = 48.0241 Factor a perfect square on the left side: (x + 6.71)(x + 6.71) = 48.0241 Calculate the square root of the right side: 6.92994228 Break this problem into two subproblems by setting (x + 6.71) equal to 6.92994228 and -6.92994228.Subproblem 1
x + 6.71 = 6.92994228 Simplifying x + 6.71 = 6.92994228 Reorder the terms: 6.71 + x = 6.92994228 Solving 6.71 + x = 6.92994228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.71' to each side of the equation. 6.71 + -6.71 + x = 6.92994228 + -6.71 Combine like terms: 6.71 + -6.71 = 0.00 0.00 + x = 6.92994228 + -6.71 x = 6.92994228 + -6.71 Combine like terms: 6.92994228 + -6.71 = 0.21994228 x = 0.21994228 Simplifying x = 0.21994228Subproblem 2
x + 6.71 = -6.92994228 Simplifying x + 6.71 = -6.92994228 Reorder the terms: 6.71 + x = -6.92994228 Solving 6.71 + x = -6.92994228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.71' to each side of the equation. 6.71 + -6.71 + x = -6.92994228 + -6.71 Combine like terms: 6.71 + -6.71 = 0.00 0.00 + x = -6.92994228 + -6.71 x = -6.92994228 + -6.71 Combine like terms: -6.92994228 + -6.71 = -13.63994228 x = -13.63994228 Simplifying x = -13.63994228Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.21994228, -13.63994228}
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