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Simplifying 7x2 + -33x + -20 = 0 Reorder the terms: -20 + -33x + 7x2 = 0 Solving -20 + -33x + 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'. -2.857142857 + -4.714285714x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -4.714285714x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -4.714285714x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -4.714285714x + x2 = 0 + 2.857142857 -4.714285714x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -4.714285714x + x2 = 2.857142857 The x term is -4.714285714x. Take half its coefficient (-2.357142857). Square it (5.556122448) and add it to both sides. Add '5.556122448' to each side of the equation. -4.714285714x + 5.556122448 + x2 = 2.857142857 + 5.556122448 Reorder the terms: 5.556122448 + -4.714285714x + x2 = 2.857142857 + 5.556122448 Combine like terms: 2.857142857 + 5.556122448 = 8.413265305 5.556122448 + -4.714285714x + x2 = 8.413265305 Factor a perfect square on the left side: (x + -2.357142857)(x + -2.357142857) = 8.413265305 Calculate the square root of the right side: 2.900562929 Break this problem into two subproblems by setting (x + -2.357142857) equal to 2.900562929 and -2.900562929.Subproblem 1
x + -2.357142857 = 2.900562929 Simplifying x + -2.357142857 = 2.900562929 Reorder the terms: -2.357142857 + x = 2.900562929 Solving -2.357142857 + x = 2.900562929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + x = 2.900562929 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + x = 2.900562929 + 2.357142857 x = 2.900562929 + 2.357142857 Combine like terms: 2.900562929 + 2.357142857 = 5.257705786 x = 5.257705786 Simplifying x = 5.257705786Subproblem 2
x + -2.357142857 = -2.900562929 Simplifying x + -2.357142857 = -2.900562929 Reorder the terms: -2.357142857 + x = -2.900562929 Solving -2.357142857 + x = -2.900562929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + x = -2.900562929 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + x = -2.900562929 + 2.357142857 x = -2.900562929 + 2.357142857 Combine like terms: -2.900562929 + 2.357142857 = -0.543420072 x = -0.543420072 Simplifying x = -0.543420072Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.257705786, -0.543420072}
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