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Simplifying 6x2 + 28x + 49 = 1936 Reorder the terms: 49 + 28x + 6x2 = 1936 Solving 49 + 28x + 6x2 = 1936 Solving for variable 'x'. Reorder the terms: 49 + -1936 + 28x + 6x2 = 1936 + -1936 Combine like terms: 49 + -1936 = -1887 -1887 + 28x + 6x2 = 1936 + -1936 Combine like terms: 1936 + -1936 = 0 -1887 + 28x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -314.5 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '314.5' to each side of the equation. -314.5 + 4.666666667x + 314.5 + x2 = 0 + 314.5 Reorder the terms: -314.5 + 314.5 + 4.666666667x + x2 = 0 + 314.5 Combine like terms: -314.5 + 314.5 = 0.0 0.0 + 4.666666667x + x2 = 0 + 314.5 4.666666667x + x2 = 0 + 314.5 Combine like terms: 0 + 314.5 = 314.5 4.666666667x + x2 = 314.5 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 314.5 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 314.5 + 5.444444448 Combine like terms: 314.5 + 5.444444448 = 319.944444448 5.444444448 + 4.666666667x + x2 = 319.944444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 319.944444448 Calculate the square root of the right side: 17.886990928 Break this problem into two subproblems by setting (x + 2.333333334) equal to 17.886990928 and -17.886990928.Subproblem 1
x + 2.333333334 = 17.886990928 Simplifying x + 2.333333334 = 17.886990928 Reorder the terms: 2.333333334 + x = 17.886990928 Solving 2.333333334 + x = 17.886990928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 17.886990928 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 17.886990928 + -2.333333334 x = 17.886990928 + -2.333333334 Combine like terms: 17.886990928 + -2.333333334 = 15.553657594 x = 15.553657594 Simplifying x = 15.553657594Subproblem 2
x + 2.333333334 = -17.886990928 Simplifying x + 2.333333334 = -17.886990928 Reorder the terms: 2.333333334 + x = -17.886990928 Solving 2.333333334 + x = -17.886990928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -17.886990928 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -17.886990928 + -2.333333334 x = -17.886990928 + -2.333333334 Combine like terms: -17.886990928 + -2.333333334 = -20.220324262 x = -20.220324262 Simplifying x = -20.220324262Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.553657594, -20.220324262}
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