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Simplifying 7x2 + -120x + -3600 = 0 Reorder the terms: -3600 + -120x + 7x2 = 0 Solving -3600 + -120x + 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'. -514.2857143 + -17.14285714x + x2 = 0 Move the constant term to the right: Add '514.2857143' to each side of the equation. -514.2857143 + -17.14285714x + 514.2857143 + x2 = 0 + 514.2857143 Reorder the terms: -514.2857143 + 514.2857143 + -17.14285714x + x2 = 0 + 514.2857143 Combine like terms: -514.2857143 + 514.2857143 = 0.0000000 0.0000000 + -17.14285714x + x2 = 0 + 514.2857143 -17.14285714x + x2 = 0 + 514.2857143 Combine like terms: 0 + 514.2857143 = 514.2857143 -17.14285714x + x2 = 514.2857143 The x term is -17.14285714x. Take half its coefficient (-8.57142857). Square it (73.46938773) and add it to both sides. Add '73.46938773' to each side of the equation. -17.14285714x + 73.46938773 + x2 = 514.2857143 + 73.46938773 Reorder the terms: 73.46938773 + -17.14285714x + x2 = 514.2857143 + 73.46938773 Combine like terms: 514.2857143 + 73.46938773 = 587.75510203 73.46938773 + -17.14285714x + x2 = 587.75510203 Factor a perfect square on the left side: (x + -8.57142857)(x + -8.57142857) = 587.75510203 Calculate the square root of the right side: 24.243661069 Break this problem into two subproblems by setting (x + -8.57142857) equal to 24.243661069 and -24.243661069.Subproblem 1
x + -8.57142857 = 24.243661069 Simplifying x + -8.57142857 = 24.243661069 Reorder the terms: -8.57142857 + x = 24.243661069 Solving -8.57142857 + x = 24.243661069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.57142857' to each side of the equation. -8.57142857 + 8.57142857 + x = 24.243661069 + 8.57142857 Combine like terms: -8.57142857 + 8.57142857 = 0.00000000 0.00000000 + x = 24.243661069 + 8.57142857 x = 24.243661069 + 8.57142857 Combine like terms: 24.243661069 + 8.57142857 = 32.815089639 x = 32.815089639 Simplifying x = 32.815089639Subproblem 2
x + -8.57142857 = -24.243661069 Simplifying x + -8.57142857 = -24.243661069 Reorder the terms: -8.57142857 + x = -24.243661069 Solving -8.57142857 + x = -24.243661069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.57142857' to each side of the equation. -8.57142857 + 8.57142857 + x = -24.243661069 + 8.57142857 Combine like terms: -8.57142857 + 8.57142857 = 0.00000000 0.00000000 + x = -24.243661069 + 8.57142857 x = -24.243661069 + 8.57142857 Combine like terms: -24.243661069 + 8.57142857 = -15.672232499 x = -15.672232499 Simplifying x = -15.672232499Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.815089639, -15.672232499}
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