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Simplifying -14x2 + 12x + -2 = 0 Reorder the terms: -2 + 12x + -14x2 = 0 Solving -2 + 12x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 6x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 6x + -7x2)' equal to zero and attempt to solve: Simplifying -1 + 6x + -7x2 = 0 Solving -1 + 6x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.1428571429 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.8571428571x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -0.8571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + -0.1428571429 -0.8571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -0.8571428571x + x2 = -0.1428571429 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = -0.1428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = -0.1428571429 + 0.1836734694 Combine like terms: -0.1428571429 + 0.1836734694 = 0.0408163265 0.1836734694 + -0.8571428571x + x2 = 0.0408163265 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.0408163265 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.202030509 and -0.202030509.Subproblem 1
x + -0.4285714286 = 0.202030509 Simplifying x + -0.4285714286 = 0.202030509 Reorder the terms: -0.4285714286 + x = 0.202030509 Solving -0.4285714286 + x = 0.202030509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 0.202030509 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.202030509 + 0.4285714286 x = 0.202030509 + 0.4285714286 Combine like terms: 0.202030509 + 0.4285714286 = 0.6306019376 x = 0.6306019376 Simplifying x = 0.6306019376Subproblem 2
x + -0.4285714286 = -0.202030509 Simplifying x + -0.4285714286 = -0.202030509 Reorder the terms: -0.4285714286 + x = -0.202030509 Solving -0.4285714286 + x = -0.202030509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -0.202030509 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.202030509 + 0.4285714286 x = -0.202030509 + 0.4285714286 Combine like terms: -0.202030509 + 0.4285714286 = 0.2265409196 x = 0.2265409196 Simplifying x = 0.2265409196Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6306019376, 0.2265409196}Solution
x = {0.6306019376, 0.2265409196}
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