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Simplifying -9x2 + 5880x + 16000 = 0 Reorder the terms: 16000 + 5880x + -9x2 = 0 Solving 16000 + 5880x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1777.777778 + -653.3333333x + x2 = 0 Move the constant term to the right: Add '1777.777778' to each side of the equation. -1777.777778 + -653.3333333x + 1777.777778 + x2 = 0 + 1777.777778 Reorder the terms: -1777.777778 + 1777.777778 + -653.3333333x + x2 = 0 + 1777.777778 Combine like terms: -1777.777778 + 1777.777778 = 0.000000 0.000000 + -653.3333333x + x2 = 0 + 1777.777778 -653.3333333x + x2 = 0 + 1777.777778 Combine like terms: 0 + 1777.777778 = 1777.777778 -653.3333333x + x2 = 1777.777778 The x term is -653.3333333x. Take half its coefficient (-326.6666667). Square it (106711.1111) and add it to both sides. Add '106711.1111' to each side of the equation. -653.3333333x + 106711.1111 + x2 = 1777.777778 + 106711.1111 Reorder the terms: 106711.1111 + -653.3333333x + x2 = 1777.777778 + 106711.1111 Combine like terms: 1777.777778 + 106711.1111 = 108488.888878 106711.1111 + -653.3333333x + x2 = 108488.888878 Factor a perfect square on the left side: (x + -326.6666667)(x + -326.6666667) = 108488.888878 Calculate the square root of the right side: 329.376515371 Break this problem into two subproblems by setting (x + -326.6666667) equal to 329.376515371 and -329.376515371.Subproblem 1
x + -326.6666667 = 329.376515371 Simplifying x + -326.6666667 = 329.376515371 Reorder the terms: -326.6666667 + x = 329.376515371 Solving -326.6666667 + x = 329.376515371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '326.6666667' to each side of the equation. -326.6666667 + 326.6666667 + x = 329.376515371 + 326.6666667 Combine like terms: -326.6666667 + 326.6666667 = 0.0000000 0.0000000 + x = 329.376515371 + 326.6666667 x = 329.376515371 + 326.6666667 Combine like terms: 329.376515371 + 326.6666667 = 656.043182071 x = 656.043182071 Simplifying x = 656.043182071Subproblem 2
x + -326.6666667 = -329.376515371 Simplifying x + -326.6666667 = -329.376515371 Reorder the terms: -326.6666667 + x = -329.376515371 Solving -326.6666667 + x = -329.376515371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '326.6666667' to each side of the equation. -326.6666667 + 326.6666667 + x = -329.376515371 + 326.6666667 Combine like terms: -326.6666667 + 326.6666667 = 0.0000000 0.0000000 + x = -329.376515371 + 326.6666667 x = -329.376515371 + 326.6666667 Combine like terms: -329.376515371 + 326.6666667 = -2.709848671 x = -2.709848671 Simplifying x = -2.709848671Solution
The solution to the problem is based on the solutions from the subproblems. x = {656.043182071, -2.709848671}
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