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Simplifying 7x2 + -19x + -5000 = 0 Reorder the terms: -5000 + -19x + 7x2 = 0 Solving -5000 + -19x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -714.2857143 + -2.714285714x + x2 = 0 Move the constant term to the right: Add '714.2857143' to each side of the equation. -714.2857143 + -2.714285714x + 714.2857143 + x2 = 0 + 714.2857143 Reorder the terms: -714.2857143 + 714.2857143 + -2.714285714x + x2 = 0 + 714.2857143 Combine like terms: -714.2857143 + 714.2857143 = 0.0000000 0.0000000 + -2.714285714x + x2 = 0 + 714.2857143 -2.714285714x + x2 = 0 + 714.2857143 Combine like terms: 0 + 714.2857143 = 714.2857143 -2.714285714x + x2 = 714.2857143 The x term is -2.714285714x. Take half its coefficient (-1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. -2.714285714x + 1.841836734 + x2 = 714.2857143 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = 714.2857143 + 1.841836734 Combine like terms: 714.2857143 + 1.841836734 = 716.127551034 1.841836734 + -2.714285714x + x2 = 716.127551034 Factor a perfect square on the left side: (x + -1.357142857)(x + -1.357142857) = 716.127551034 Calculate the square root of the right side: 26.760559617 Break this problem into two subproblems by setting (x + -1.357142857) equal to 26.760559617 and -26.760559617.Subproblem 1
x + -1.357142857 = 26.760559617 Simplifying x + -1.357142857 = 26.760559617 Reorder the terms: -1.357142857 + x = 26.760559617 Solving -1.357142857 + x = 26.760559617 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + x = 26.760559617 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 26.760559617 + 1.357142857 x = 26.760559617 + 1.357142857 Combine like terms: 26.760559617 + 1.357142857 = 28.117702474 x = 28.117702474 Simplifying x = 28.117702474Subproblem 2
x + -1.357142857 = -26.760559617 Simplifying x + -1.357142857 = -26.760559617 Reorder the terms: -1.357142857 + x = -26.760559617 Solving -1.357142857 + x = -26.760559617 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + x = -26.760559617 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -26.760559617 + 1.357142857 x = -26.760559617 + 1.357142857 Combine like terms: -26.760559617 + 1.357142857 = -25.40341676 x = -25.40341676 Simplifying x = -25.40341676Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.117702474, -25.40341676}
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