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Simplifying 14x2 + 30x + -12 = 0 Reorder the terms: -12 + 30x + 14x2 = 0 Solving -12 + 30x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 15x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 15x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + 15x + 7x2 = 0 Solving -6 + 15x + 7x2 = 0 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 = 0.344587686 x = 0.344587686 Simplifying x = 0.344587686Subproblem 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 = -2.48744483 x = -2.48744483 Simplifying x = -2.48744483Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.344587686, -2.48744483}Solution
x = {0.344587686, -2.48744483}
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