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Simplifying (7x2) + -19x + -48 = 0 Reorder the terms: -48 + -19x + (7x2) = 0 Solving -48 + -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'. -6.857142857 + -2.714285714x + x2 = 0 Move the constant term to the right: Add '6.857142857' to each side of the equation. -6.857142857 + -2.714285714x + 6.857142857 + x2 = 0 + 6.857142857 Reorder the terms: -6.857142857 + 6.857142857 + -2.714285714x + x2 = 0 + 6.857142857 Combine like terms: -6.857142857 + 6.857142857 = 0.000000000 0.000000000 + -2.714285714x + x2 = 0 + 6.857142857 -2.714285714x + x2 = 0 + 6.857142857 Combine like terms: 0 + 6.857142857 = 6.857142857 -2.714285714x + x2 = 6.857142857 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 = 6.857142857 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = 6.857142857 + 1.841836734 Combine like terms: 6.857142857 + 1.841836734 = 8.698979591 1.841836734 + -2.714285714x + x2 = 8.698979591 Factor a perfect square on the left side: ((x) + -1.357142857)((x) + -1.357142857) = 8.698979591 Calculate the square root of the right side: 2.94940326 Break this problem into two subproblems by setting ((x) + -1.357142857) equal to 2.94940326 and -2.94940326.Subproblem 1
(x) + -1.357142857 = 2.94940326 Simplifying (x) + -1.357142857 = 2.94940326 x + -1.357142857 = 2.94940326 Reorder the terms: -1.357142857 + x = 2.94940326 Solving -1.357142857 + x = 2.94940326 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 = 2.94940326 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 2.94940326 + 1.357142857 x = 2.94940326 + 1.357142857 Combine like terms: 2.94940326 + 1.357142857 = 4.306546117 x = 4.306546117 Simplifying x = 4.306546117Subproblem 2
(x) + -1.357142857 = -2.94940326 Simplifying (x) + -1.357142857 = -2.94940326 x + -1.357142857 = -2.94940326 Reorder the terms: -1.357142857 + x = -2.94940326 Solving -1.357142857 + x = -2.94940326 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 = -2.94940326 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -2.94940326 + 1.357142857 x = -2.94940326 + 1.357142857 Combine like terms: -2.94940326 + 1.357142857 = -1.592260403 x = -1.592260403 Simplifying x = -1.592260403Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.306546117, -1.592260403}
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