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Simplifying 6x2 + -14x + -8000 = 0 Reorder the terms: -8000 + -14x + 6x2 = 0 Solving -8000 + -14x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4000 + -7x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4000 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying -4000 + -7x + 3x2 = 0 Solving -4000 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1333.333333 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '1333.333333' to each side of the equation. -1333.333333 + -2.333333333x + 1333.333333 + x2 = 0 + 1333.333333 Reorder the terms: -1333.333333 + 1333.333333 + -2.333333333x + x2 = 0 + 1333.333333 Combine like terms: -1333.333333 + 1333.333333 = 0.000000 0.000000 + -2.333333333x + x2 = 0 + 1333.333333 -2.333333333x + x2 = 0 + 1333.333333 Combine like terms: 0 + 1333.333333 = 1333.333333 -2.333333333x + x2 = 1333.333333 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 1333.333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 1333.333333 + 1.361111112 Combine like terms: 1333.333333 + 1.361111112 = 1334.694444112 1.361111112 + -2.333333333x + x2 = 1334.694444112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 1334.694444112 Calculate the square root of the right side: 36.53347019 Break this problem into two subproblems by setting (x + -1.166666667) equal to 36.53347019 and -36.53347019.Subproblem 1
x + -1.166666667 = 36.53347019 Simplifying x + -1.166666667 = 36.53347019 Reorder the terms: -1.166666667 + x = 36.53347019 Solving -1.166666667 + x = 36.53347019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 36.53347019 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 36.53347019 + 1.166666667 x = 36.53347019 + 1.166666667 Combine like terms: 36.53347019 + 1.166666667 = 37.700136857 x = 37.700136857 Simplifying x = 37.700136857Subproblem 2
x + -1.166666667 = -36.53347019 Simplifying x + -1.166666667 = -36.53347019 Reorder the terms: -1.166666667 + x = -36.53347019 Solving -1.166666667 + x = -36.53347019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -36.53347019 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -36.53347019 + 1.166666667 x = -36.53347019 + 1.166666667 Combine like terms: -36.53347019 + 1.166666667 = -35.366803523 x = -35.366803523 Simplifying x = -35.366803523Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.700136857, -35.366803523}Solution
x = {37.700136857, -35.366803523}
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