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Simplifying 3x(x + -50) + 5x = 1300 Reorder the terms: 3x(-50 + x) + 5x = 1300 (-50 * 3x + x * 3x) + 5x = 1300 (-150x + 3x2) + 5x = 1300 Reorder the terms: -150x + 5x + 3x2 = 1300 Combine like terms: -150x + 5x = -145x -145x + 3x2 = 1300 Solving -145x + 3x2 = 1300 Solving for variable 'x'. Reorder the terms: -1300 + -145x + 3x2 = 1300 + -1300 Combine like terms: 1300 + -1300 = 0 -1300 + -145x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -433.3333333 + -48.33333333x + x2 = 0 Move the constant term to the right: Add '433.3333333' to each side of the equation. -433.3333333 + -48.33333333x + 433.3333333 + x2 = 0 + 433.3333333 Reorder the terms: -433.3333333 + 433.3333333 + -48.33333333x + x2 = 0 + 433.3333333 Combine like terms: -433.3333333 + 433.3333333 = 0.0000000 0.0000000 + -48.33333333x + x2 = 0 + 433.3333333 -48.33333333x + x2 = 0 + 433.3333333 Combine like terms: 0 + 433.3333333 = 433.3333333 -48.33333333x + x2 = 433.3333333 The x term is -48.33333333x. Take half its coefficient (-24.16666667). Square it (584.0277779) and add it to both sides. Add '584.0277779' to each side of the equation. -48.33333333x + 584.0277779 + x2 = 433.3333333 + 584.0277779 Reorder the terms: 584.0277779 + -48.33333333x + x2 = 433.3333333 + 584.0277779 Combine like terms: 433.3333333 + 584.0277779 = 1017.3611112 584.0277779 + -48.33333333x + x2 = 1017.3611112 Factor a perfect square on the left side: (x + -24.16666667)(x + -24.16666667) = 1017.3611112 Calculate the square root of the right side: 31.896098683 Break this problem into two subproblems by setting (x + -24.16666667) equal to 31.896098683 and -31.896098683.Subproblem 1
x + -24.16666667 = 31.896098683 Simplifying x + -24.16666667 = 31.896098683 Reorder the terms: -24.16666667 + x = 31.896098683 Solving -24.16666667 + x = 31.896098683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.16666667' to each side of the equation. -24.16666667 + 24.16666667 + x = 31.896098683 + 24.16666667 Combine like terms: -24.16666667 + 24.16666667 = 0.00000000 0.00000000 + x = 31.896098683 + 24.16666667 x = 31.896098683 + 24.16666667 Combine like terms: 31.896098683 + 24.16666667 = 56.062765353 x = 56.062765353 Simplifying x = 56.062765353Subproblem 2
x + -24.16666667 = -31.896098683 Simplifying x + -24.16666667 = -31.896098683 Reorder the terms: -24.16666667 + x = -31.896098683 Solving -24.16666667 + x = -31.896098683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.16666667' to each side of the equation. -24.16666667 + 24.16666667 + x = -31.896098683 + 24.16666667 Combine like terms: -24.16666667 + 24.16666667 = 0.00000000 0.00000000 + x = -31.896098683 + 24.16666667 x = -31.896098683 + 24.16666667 Combine like terms: -31.896098683 + 24.16666667 = -7.729432013 x = -7.729432013 Simplifying x = -7.729432013Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.062765353, -7.729432013}
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