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Simplifying 0.70x2 + -9x + -4000 = 0 Reorder the terms: -4000 + -9x + 0.70x2 = 0 Solving -4000 + -9x + 0.70x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.70 the coefficient of the squared term: Divide each side by '0.70'. -5714.285714 + -12.85714286x + x2 = 0 Move the constant term to the right: Add '5714.285714' to each side of the equation. -5714.285714 + -12.85714286x + 5714.285714 + x2 = 0 + 5714.285714 Reorder the terms: -5714.285714 + 5714.285714 + -12.85714286x + x2 = 0 + 5714.285714 Combine like terms: -5714.285714 + 5714.285714 = 0.000000 0.000000 + -12.85714286x + x2 = 0 + 5714.285714 -12.85714286x + x2 = 0 + 5714.285714 Combine like terms: 0 + 5714.285714 = 5714.285714 -12.85714286x + x2 = 5714.285714 The x term is -12.85714286x. Take half its coefficient (-6.42857143). Square it (41.32653063) and add it to both sides. Add '41.32653063' to each side of the equation. -12.85714286x + 41.32653063 + x2 = 5714.285714 + 41.32653063 Reorder the terms: 41.32653063 + -12.85714286x + x2 = 5714.285714 + 41.32653063 Combine like terms: 5714.285714 + 41.32653063 = 5755.61224463 41.32653063 + -12.85714286x + x2 = 5755.61224463 Factor a perfect square on the left side: (x + -6.42857143)(x + -6.42857143) = 5755.61224463 Calculate the square root of the right side: 75.86575146 Break this problem into two subproblems by setting (x + -6.42857143) equal to 75.86575146 and -75.86575146.Subproblem 1
x + -6.42857143 = 75.86575146 Simplifying x + -6.42857143 = 75.86575146 Reorder the terms: -6.42857143 + x = 75.86575146 Solving -6.42857143 + x = 75.86575146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + x = 75.86575146 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + x = 75.86575146 + 6.42857143 x = 75.86575146 + 6.42857143 Combine like terms: 75.86575146 + 6.42857143 = 82.29432289 x = 82.29432289 Simplifying x = 82.29432289Subproblem 2
x + -6.42857143 = -75.86575146 Simplifying x + -6.42857143 = -75.86575146 Reorder the terms: -6.42857143 + x = -75.86575146 Solving -6.42857143 + x = -75.86575146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + x = -75.86575146 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + x = -75.86575146 + 6.42857143 x = -75.86575146 + 6.42857143 Combine like terms: -75.86575146 + 6.42857143 = -69.43718003 x = -69.43718003 Simplifying x = -69.43718003Solution
The solution to the problem is based on the solutions from the subproblems. x = {82.29432289, -69.43718003}
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