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Simplifying 13x2 + -73x = 380 Reorder the terms: -73x + 13x2 = 380 Solving -73x + 13x2 = 380 Solving for variable 'x'. Reorder the terms: -380 + -73x + 13x2 = 380 + -380 Combine like terms: 380 + -380 = 0 -380 + -73x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -29.23076923 + -5.615384615x + x2 = 0 Move the constant term to the right: Add '29.23076923' to each side of the equation. -29.23076923 + -5.615384615x + 29.23076923 + x2 = 0 + 29.23076923 Reorder the terms: -29.23076923 + 29.23076923 + -5.615384615x + x2 = 0 + 29.23076923 Combine like terms: -29.23076923 + 29.23076923 = 0.00000000 0.00000000 + -5.615384615x + x2 = 0 + 29.23076923 -5.615384615x + x2 = 0 + 29.23076923 Combine like terms: 0 + 29.23076923 = 29.23076923 -5.615384615x + x2 = 29.23076923 The x term is -5.615384615x. Take half its coefficient (-2.807692308). Square it (7.883136096) and add it to both sides. Add '7.883136096' to each side of the equation. -5.615384615x + 7.883136096 + x2 = 29.23076923 + 7.883136096 Reorder the terms: 7.883136096 + -5.615384615x + x2 = 29.23076923 + 7.883136096 Combine like terms: 29.23076923 + 7.883136096 = 37.113905326 7.883136096 + -5.615384615x + x2 = 37.113905326 Factor a perfect square on the left side: (x + -2.807692308)(x + -2.807692308) = 37.113905326 Calculate the square root of the right side: 6.092118295 Break this problem into two subproblems by setting (x + -2.807692308) equal to 6.092118295 and -6.092118295.Subproblem 1
x + -2.807692308 = 6.092118295 Simplifying x + -2.807692308 = 6.092118295 Reorder the terms: -2.807692308 + x = 6.092118295 Solving -2.807692308 + x = 6.092118295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.807692308' to each side of the equation. -2.807692308 + 2.807692308 + x = 6.092118295 + 2.807692308 Combine like terms: -2.807692308 + 2.807692308 = 0.000000000 0.000000000 + x = 6.092118295 + 2.807692308 x = 6.092118295 + 2.807692308 Combine like terms: 6.092118295 + 2.807692308 = 8.899810603 x = 8.899810603 Simplifying x = 8.899810603Subproblem 2
x + -2.807692308 = -6.092118295 Simplifying x + -2.807692308 = -6.092118295 Reorder the terms: -2.807692308 + x = -6.092118295 Solving -2.807692308 + x = -6.092118295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.807692308' to each side of the equation. -2.807692308 + 2.807692308 + x = -6.092118295 + 2.807692308 Combine like terms: -2.807692308 + 2.807692308 = 0.000000000 0.000000000 + x = -6.092118295 + 2.807692308 x = -6.092118295 + 2.807692308 Combine like terms: -6.092118295 + 2.807692308 = -3.284425987 x = -3.284425987 Simplifying x = -3.284425987Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.899810603, -3.284425987}
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