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Simplifying 6x2 + -4x + -210 = 0 Reorder the terms: -210 + -4x + 6x2 = 0 Solving -210 + -4x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-105 + -2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-105 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -105 + -2x + 3x2 = 0 Solving -105 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -35 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -0.6666666667x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -0.6666666667x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -0.6666666667x + x2 = 0 + 35 -0.6666666667x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -0.6666666667x + x2 = 35 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 35 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 35 + 0.1111111112 Combine like terms: 35 + 0.1111111112 = 35.1111111112 0.1111111112 + -0.6666666667x + x2 = 35.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 35.1111111112 Calculate the square root of the right side: 5.925462945 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 5.925462945 and -5.925462945.Subproblem 1
x + -0.3333333334 = 5.925462945 Simplifying x + -0.3333333334 = 5.925462945 Reorder the terms: -0.3333333334 + x = 5.925462945 Solving -0.3333333334 + x = 5.925462945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 5.925462945 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 5.925462945 + 0.3333333334 x = 5.925462945 + 0.3333333334 Combine like terms: 5.925462945 + 0.3333333334 = 6.2587962784 x = 6.2587962784 Simplifying x = 6.2587962784Subproblem 2
x + -0.3333333334 = -5.925462945 Simplifying x + -0.3333333334 = -5.925462945 Reorder the terms: -0.3333333334 + x = -5.925462945 Solving -0.3333333334 + x = -5.925462945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -5.925462945 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -5.925462945 + 0.3333333334 x = -5.925462945 + 0.3333333334 Combine like terms: -5.925462945 + 0.3333333334 = -5.5921296116 x = -5.5921296116 Simplifying x = -5.5921296116Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.2587962784, -5.5921296116}Solution
x = {6.2587962784, -5.5921296116}
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