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Simplifying 6x2 + -2x + -1200 = 0 Reorder the terms: -1200 + -2x + 6x2 = 0 Solving -1200 + -2x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-600 + -1x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-600 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -600 + -1x + 3x2 = 0 Solving -600 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -200 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -0.3333333333x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -0.3333333333x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -0.3333333333x + x2 = 0 + 200 -0.3333333333x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -0.3333333333x + x2 = 200 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 200 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 200 + 0.02777777779 Combine like terms: 200 + 0.02777777779 = 200.02777777779 0.02777777779 + -0.3333333333x + x2 = 200.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 200.02777777779 Calculate the square root of the right side: 14.143117682 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 14.143117682 and -14.143117682.Subproblem 1
x + -0.1666666667 = 14.143117682 Simplifying x + -0.1666666667 = 14.143117682 Reorder the terms: -0.1666666667 + x = 14.143117682 Solving -0.1666666667 + x = 14.143117682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 14.143117682 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 14.143117682 + 0.1666666667 x = 14.143117682 + 0.1666666667 Combine like terms: 14.143117682 + 0.1666666667 = 14.3097843487 x = 14.3097843487 Simplifying x = 14.3097843487Subproblem 2
x + -0.1666666667 = -14.143117682 Simplifying x + -0.1666666667 = -14.143117682 Reorder the terms: -0.1666666667 + x = -14.143117682 Solving -0.1666666667 + x = -14.143117682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -14.143117682 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -14.143117682 + 0.1666666667 x = -14.143117682 + 0.1666666667 Combine like terms: -14.143117682 + 0.1666666667 = -13.9764510153 x = -13.9764510153 Simplifying x = -13.9764510153Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.3097843487, -13.9764510153}Solution
x = {14.3097843487, -13.9764510153}
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