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Simplifying 6 + 15x + -7x2 = 0 Solving 6 + 15x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.8571428571 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -2.142857143x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -2.142857143x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -2.142857143x + x2 = 0 + 0.8571428571 -2.142857143x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -2.142857143x + x2 = 0.8571428571 The x term is -2.142857143x. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143x + 1.147959185 + x2 = 0.8571428571 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = 0.8571428571 + 1.147959185 Combine like terms: 0.8571428571 + 1.147959185 = 2.0051020421 1.147959185 + -2.142857143x + x2 = 2.0051020421 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 2.0051020421 Calculate the square root of the right side: 1.416016258 Break this problem into two subproblems by setting (x + -1.071428572) equal to 1.416016258 and -1.416016258.Subproblem 1
x + -1.071428572 = 1.416016258 Simplifying x + -1.071428572 = 1.416016258 Reorder the terms: -1.071428572 + x = 1.416016258 Solving -1.071428572 + x = 1.416016258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = 1.416016258 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.416016258 + 1.071428572 x = 1.416016258 + 1.071428572 Combine like terms: 1.416016258 + 1.071428572 = 2.48744483 x = 2.48744483 Simplifying x = 2.48744483Subproblem 2
x + -1.071428572 = -1.416016258 Simplifying x + -1.071428572 = -1.416016258 Reorder the terms: -1.071428572 + x = -1.416016258 Solving -1.071428572 + x = -1.416016258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = -1.416016258 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.416016258 + 1.071428572 x = -1.416016258 + 1.071428572 Combine like terms: -1.416016258 + 1.071428572 = -0.344587686 x = -0.344587686 Simplifying x = -0.344587686Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.48744483, -0.344587686}
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