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Simplifying 6x2 + 700x = 2800 Reorder the terms: 700x + 6x2 = 2800 Solving 700x + 6x2 = 2800 Solving for variable 'x'. Reorder the terms: -2800 + 700x + 6x2 = 2800 + -2800 Combine like terms: 2800 + -2800 = 0 -2800 + 700x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1400 + 350x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1400 + 350x + 3x2)' equal to zero and attempt to solve: Simplifying -1400 + 350x + 3x2 = 0 Solving -1400 + 350x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -466.6666667 + 116.6666667x + x2 = 0 Move the constant term to the right: Add '466.6666667' to each side of the equation. -466.6666667 + 116.6666667x + 466.6666667 + x2 = 0 + 466.6666667 Reorder the terms: -466.6666667 + 466.6666667 + 116.6666667x + x2 = 0 + 466.6666667 Combine like terms: -466.6666667 + 466.6666667 = 0.0000000 0.0000000 + 116.6666667x + x2 = 0 + 466.6666667 116.6666667x + x2 = 0 + 466.6666667 Combine like terms: 0 + 466.6666667 = 466.6666667 116.6666667x + x2 = 466.6666667 The x term is 116.6666667x. Take half its coefficient (58.33333335). Square it (3402.777780) and add it to both sides. Add '3402.777780' to each side of the equation. 116.6666667x + 3402.777780 + x2 = 466.6666667 + 3402.777780 Reorder the terms: 3402.777780 + 116.6666667x + x2 = 466.6666667 + 3402.777780 Combine like terms: 466.6666667 + 3402.777780 = 3869.4444467 3402.777780 + 116.6666667x + x2 = 3869.4444467 Factor a perfect square on the left side: (x + 58.33333335)(x + 58.33333335) = 3869.4444467 Calculate the square root of the right side: 62.204858707 Break this problem into two subproblems by setting (x + 58.33333335) equal to 62.204858707 and -62.204858707.Subproblem 1
x + 58.33333335 = 62.204858707 Simplifying x + 58.33333335 = 62.204858707 Reorder the terms: 58.33333335 + x = 62.204858707 Solving 58.33333335 + x = 62.204858707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-58.33333335' to each side of the equation. 58.33333335 + -58.33333335 + x = 62.204858707 + -58.33333335 Combine like terms: 58.33333335 + -58.33333335 = 0.00000000 0.00000000 + x = 62.204858707 + -58.33333335 x = 62.204858707 + -58.33333335 Combine like terms: 62.204858707 + -58.33333335 = 3.871525357 x = 3.871525357 Simplifying x = 3.871525357Subproblem 2
x + 58.33333335 = -62.204858707 Simplifying x + 58.33333335 = -62.204858707 Reorder the terms: 58.33333335 + x = -62.204858707 Solving 58.33333335 + x = -62.204858707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-58.33333335' to each side of the equation. 58.33333335 + -58.33333335 + x = -62.204858707 + -58.33333335 Combine like terms: 58.33333335 + -58.33333335 = 0.00000000 0.00000000 + x = -62.204858707 + -58.33333335 x = -62.204858707 + -58.33333335 Combine like terms: -62.204858707 + -58.33333335 = -120.538192057 x = -120.538192057 Simplifying x = -120.538192057Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.871525357, -120.538192057}Solution
x = {3.871525357, -120.538192057}
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