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Simplifying 7x2 + -61x + -36 = 0 Reorder the terms: -36 + -61x + 7x2 = 0 Solving -36 + -61x + 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'. -5.142857143 + -8.714285714x + x2 = 0 Move the constant term to the right: Add '5.142857143' to each side of the equation. -5.142857143 + -8.714285714x + 5.142857143 + x2 = 0 + 5.142857143 Reorder the terms: -5.142857143 + 5.142857143 + -8.714285714x + x2 = 0 + 5.142857143 Combine like terms: -5.142857143 + 5.142857143 = 0.000000000 0.000000000 + -8.714285714x + x2 = 0 + 5.142857143 -8.714285714x + x2 = 0 + 5.142857143 Combine like terms: 0 + 5.142857143 = 5.142857143 -8.714285714x + x2 = 5.142857143 The x term is -8.714285714x. Take half its coefficient (-4.357142857). Square it (18.98469388) and add it to both sides. Add '18.98469388' to each side of the equation. -8.714285714x + 18.98469388 + x2 = 5.142857143 + 18.98469388 Reorder the terms: 18.98469388 + -8.714285714x + x2 = 5.142857143 + 18.98469388 Combine like terms: 5.142857143 + 18.98469388 = 24.127551023 18.98469388 + -8.714285714x + x2 = 24.127551023 Factor a perfect square on the left side: (x + -4.357142857)(x + -4.357142857) = 24.127551023 Calculate the square root of the right side: 4.911980357 Break this problem into two subproblems by setting (x + -4.357142857) equal to 4.911980357 and -4.911980357.Subproblem 1
x + -4.357142857 = 4.911980357 Simplifying x + -4.357142857 = 4.911980357 Reorder the terms: -4.357142857 + x = 4.911980357 Solving -4.357142857 + x = 4.911980357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.357142857' to each side of the equation. -4.357142857 + 4.357142857 + x = 4.911980357 + 4.357142857 Combine like terms: -4.357142857 + 4.357142857 = 0.000000000 0.000000000 + x = 4.911980357 + 4.357142857 x = 4.911980357 + 4.357142857 Combine like terms: 4.911980357 + 4.357142857 = 9.269123214 x = 9.269123214 Simplifying x = 9.269123214Subproblem 2
x + -4.357142857 = -4.911980357 Simplifying x + -4.357142857 = -4.911980357 Reorder the terms: -4.357142857 + x = -4.911980357 Solving -4.357142857 + x = -4.911980357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.357142857' to each side of the equation. -4.357142857 + 4.357142857 + x = -4.911980357 + 4.357142857 Combine like terms: -4.357142857 + 4.357142857 = 0.000000000 0.000000000 + x = -4.911980357 + 4.357142857 x = -4.911980357 + 4.357142857 Combine like terms: -4.911980357 + 4.357142857 = -0.5548375 x = -0.5548375 Simplifying x = -0.5548375Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.269123214, -0.5548375}
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