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Simplifying 14x2 + -6x + -12 = 0 Reorder the terms: -12 + -6x + 14x2 = 0 Solving -12 + -6x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -3x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -3x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + -3x + 7x2 = 0 Solving -6 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -0.4285714286x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -0.4285714286x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -0.4285714286x + x2 = 0 + 0.8571428571 -0.4285714286x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -0.4285714286x + x2 = 0.8571428571 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 0.8571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 0.8571428571 + 0.04591836735 Combine like terms: 0.8571428571 + 0.04591836735 = 0.90306122445 0.04591836735 + -0.4285714286x + x2 = 0.90306122445 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 0.90306122445 Calculate the square root of the right side: 0.950295335 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 0.950295335 and -0.950295335.Subproblem 1
x + -0.2142857143 = 0.950295335 Simplifying x + -0.2142857143 = 0.950295335 Reorder the terms: -0.2142857143 + x = 0.950295335 Solving -0.2142857143 + x = 0.950295335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 0.950295335 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 0.950295335 + 0.2142857143 x = 0.950295335 + 0.2142857143 Combine like terms: 0.950295335 + 0.2142857143 = 1.1645810493 x = 1.1645810493 Simplifying x = 1.1645810493Subproblem 2
x + -0.2142857143 = -0.950295335 Simplifying x + -0.2142857143 = -0.950295335 Reorder the terms: -0.2142857143 + x = -0.950295335 Solving -0.2142857143 + x = -0.950295335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -0.950295335 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -0.950295335 + 0.2142857143 x = -0.950295335 + 0.2142857143 Combine like terms: -0.950295335 + 0.2142857143 = -0.7360096207 x = -0.7360096207 Simplifying x = -0.7360096207Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1645810493, -0.7360096207}Solution
x = {1.1645810493, -0.7360096207}
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