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Simplifying 6x2 + -64x + 88 = 300 Reorder the terms: 88 + -64x + 6x2 = 300 Solving 88 + -64x + 6x2 = 300 Solving for variable 'x'. Reorder the terms: 88 + -300 + -64x + 6x2 = 300 + -300 Combine like terms: 88 + -300 = -212 -212 + -64x + 6x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -212 + -64x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-106 + -32x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-106 + -32x + 3x2)' equal to zero and attempt to solve: Simplifying -106 + -32x + 3x2 = 0 Solving -106 + -32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -35.33333333 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '35.33333333' to each side of the equation. -35.33333333 + -10.66666667x + 35.33333333 + x2 = 0 + 35.33333333 Reorder the terms: -35.33333333 + 35.33333333 + -10.66666667x + x2 = 0 + 35.33333333 Combine like terms: -35.33333333 + 35.33333333 = 0.00000000 0.00000000 + -10.66666667x + x2 = 0 + 35.33333333 -10.66666667x + x2 = 0 + 35.33333333 Combine like terms: 0 + 35.33333333 = 35.33333333 -10.66666667x + x2 = 35.33333333 The x term is -10.66666667x. Take half its coefficient (-5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. -10.66666667x + 28.44444446 + x2 = 35.33333333 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = 35.33333333 + 28.44444446 Combine like terms: 35.33333333 + 28.44444446 = 63.77777779 28.44444446 + -10.66666667x + x2 = 63.77777779 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 63.77777779 Calculate the square root of the right side: 7.986099035 Break this problem into two subproblems by setting (x + -5.333333335) equal to 7.986099035 and -7.986099035.Subproblem 1
x + -5.333333335 = 7.986099035 Simplifying x + -5.333333335 = 7.986099035 Reorder the terms: -5.333333335 + x = 7.986099035 Solving -5.333333335 + x = 7.986099035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = 7.986099035 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 7.986099035 + 5.333333335 x = 7.986099035 + 5.333333335 Combine like terms: 7.986099035 + 5.333333335 = 13.31943237 x = 13.31943237 Simplifying x = 13.31943237Subproblem 2
x + -5.333333335 = -7.986099035 Simplifying x + -5.333333335 = -7.986099035 Reorder the terms: -5.333333335 + x = -7.986099035 Solving -5.333333335 + x = -7.986099035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = -7.986099035 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -7.986099035 + 5.333333335 x = -7.986099035 + 5.333333335 Combine like terms: -7.986099035 + 5.333333335 = -2.6527657 x = -2.6527657 Simplifying x = -2.6527657Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.31943237, -2.6527657}Solution
x = {13.31943237, -2.6527657}
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