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Simplifying 7x2 + 12x + -4896 = 0 Reorder the terms: -4896 + 12x + 7x2 = 0 Solving -4896 + 12x + 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'. -699.4285714 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '699.4285714' to each side of the equation. -699.4285714 + 1.714285714x + 699.4285714 + x2 = 0 + 699.4285714 Reorder the terms: -699.4285714 + 699.4285714 + 1.714285714x + x2 = 0 + 699.4285714 Combine like terms: -699.4285714 + 699.4285714 = 0.0000000 0.0000000 + 1.714285714x + x2 = 0 + 699.4285714 1.714285714x + x2 = 0 + 699.4285714 Combine like terms: 0 + 699.4285714 = 699.4285714 1.714285714x + x2 = 699.4285714 The x term is 1.714285714x. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x + 0.7346938773 + x2 = 699.4285714 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 699.4285714 + 0.7346938773 Combine like terms: 699.4285714 + 0.7346938773 = 700.1632652773 0.7346938773 + 1.714285714x + x2 = 700.1632652773 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 700.1632652773 Calculate the square root of the right side: 26.460598354 Break this problem into two subproblems by setting (x + 0.857142857) equal to 26.460598354 and -26.460598354.Subproblem 1
x + 0.857142857 = 26.460598354 Simplifying x + 0.857142857 = 26.460598354 Reorder the terms: 0.857142857 + x = 26.460598354 Solving 0.857142857 + x = 26.460598354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = 26.460598354 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 26.460598354 + -0.857142857 x = 26.460598354 + -0.857142857 Combine like terms: 26.460598354 + -0.857142857 = 25.603455497 x = 25.603455497 Simplifying x = 25.603455497Subproblem 2
x + 0.857142857 = -26.460598354 Simplifying x + 0.857142857 = -26.460598354 Reorder the terms: 0.857142857 + x = -26.460598354 Solving 0.857142857 + x = -26.460598354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = -26.460598354 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -26.460598354 + -0.857142857 x = -26.460598354 + -0.857142857 Combine like terms: -26.460598354 + -0.857142857 = -27.317741211 x = -27.317741211 Simplifying x = -27.317741211Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.603455497, -27.317741211}
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