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Simplifying x * x + 12x + 10 = 0 Multiply x * x x2 + 12x + 10 = 0 Reorder the terms: 10 + 12x + x2 = 0 Solving 10 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 12x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 12x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 12x + x2 = 0 + -10 12x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 12x + x2 = -10 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -10 + 36 Reorder the terms: 36 + 12x + x2 = -10 + 36 Combine like terms: -10 + 36 = 26 36 + 12x + x2 = 26 Factor a perfect square on the left side: (x + 6)(x + 6) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 6) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 6 = 5.099019514 Simplifying x + 6 = 5.099019514 Reorder the terms: 6 + x = 5.099019514 Solving 6 + x = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.099019514 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.099019514 + -6 x = 5.099019514 + -6 Combine like terms: 5.099019514 + -6 = -0.900980486 x = -0.900980486 Simplifying x = -0.900980486Subproblem 2
x + 6 = -5.099019514 Simplifying x + 6 = -5.099019514 Reorder the terms: 6 + x = -5.099019514 Solving 6 + x = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.099019514 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.099019514 + -6 x = -5.099019514 + -6 Combine like terms: -5.099019514 + -6 = -11.099019514 x = -11.099019514 Simplifying x = -11.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.900980486, -11.099019514}
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