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Simplifying -9x2 + 300x + 7 = 0 Reorder the terms: 7 + 300x + -9x2 = 0 Solving 7 + 300x + -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'. -0.7777777778 + -33.33333333x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -33.33333333x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -33.33333333x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -33.33333333x + x2 = 0 + 0.7777777778 -33.33333333x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -33.33333333x + x2 = 0.7777777778 The x term is -33.33333333x. Take half its coefficient (-16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. -33.33333333x + 277.7777779 + x2 = 0.7777777778 + 277.7777779 Reorder the terms: 277.7777779 + -33.33333333x + x2 = 0.7777777778 + 277.7777779 Combine like terms: 0.7777777778 + 277.7777779 = 278.5555556778 277.7777779 + -33.33333333x + x2 = 278.5555556778 Factor a perfect square on the left side: (x + -16.66666667)(x + -16.66666667) = 278.5555556778 Calculate the square root of the right side: 16.689983693 Break this problem into two subproblems by setting (x + -16.66666667) equal to 16.689983693 and -16.689983693.Subproblem 1
x + -16.66666667 = 16.689983693 Simplifying x + -16.66666667 = 16.689983693 Reorder the terms: -16.66666667 + x = 16.689983693 Solving -16.66666667 + x = 16.689983693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = 16.689983693 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = 16.689983693 + 16.66666667 x = 16.689983693 + 16.66666667 Combine like terms: 16.689983693 + 16.66666667 = 33.356650363 x = 33.356650363 Simplifying x = 33.356650363Subproblem 2
x + -16.66666667 = -16.689983693 Simplifying x + -16.66666667 = -16.689983693 Reorder the terms: -16.66666667 + x = -16.689983693 Solving -16.66666667 + x = -16.689983693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = -16.689983693 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = -16.689983693 + 16.66666667 x = -16.689983693 + 16.66666667 Combine like terms: -16.689983693 + 16.66666667 = -0.023317023 x = -0.023317023 Simplifying x = -0.023317023Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.356650363, -0.023317023}
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