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Simplifying 0 = 3x2 + -97x + 250 Reorder the terms: 0 = 250 + -97x + 3x2 Solving 0 = 250 + -97x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -250 = -250 -250 + 97x + -3x2 = 250 + -97x + 3x2 + -250 + 97x + -3x2 Reorder the terms: -250 + 97x + -3x2 = 250 + -250 + -97x + 97x + 3x2 + -3x2 Combine like terms: 250 + -250 = 0 -250 + 97x + -3x2 = 0 + -97x + 97x + 3x2 + -3x2 -250 + 97x + -3x2 = -97x + 97x + 3x2 + -3x2 Combine like terms: -97x + 97x = 0 -250 + 97x + -3x2 = 0 + 3x2 + -3x2 -250 + 97x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -250 + 97x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 83.33333333 + -32.33333333x + x2 = 0 Move the constant term to the right: Add '-83.33333333' to each side of the equation. 83.33333333 + -32.33333333x + -83.33333333 + x2 = 0 + -83.33333333 Reorder the terms: 83.33333333 + -83.33333333 + -32.33333333x + x2 = 0 + -83.33333333 Combine like terms: 83.33333333 + -83.33333333 = 0.00000000 0.00000000 + -32.33333333x + x2 = 0 + -83.33333333 -32.33333333x + x2 = 0 + -83.33333333 Combine like terms: 0 + -83.33333333 = -83.33333333 -32.33333333x + x2 = -83.33333333 The x term is -32.33333333x. Take half its coefficient (-16.16666667). Square it (261.3611112) and add it to both sides. Add '261.3611112' to each side of the equation. -32.33333333x + 261.3611112 + x2 = -83.33333333 + 261.3611112 Reorder the terms: 261.3611112 + -32.33333333x + x2 = -83.33333333 + 261.3611112 Combine like terms: -83.33333333 + 261.3611112 = 178.02777787 261.3611112 + -32.33333333x + x2 = 178.02777787 Factor a perfect square on the left side: (x + -16.16666667)(x + -16.16666667) = 178.02777787 Calculate the square root of the right side: 13.342705043 Break this problem into two subproblems by setting (x + -16.16666667) equal to 13.342705043 and -13.342705043.Subproblem 1
x + -16.16666667 = 13.342705043 Simplifying x + -16.16666667 = 13.342705043 Reorder the terms: -16.16666667 + x = 13.342705043 Solving -16.16666667 + x = 13.342705043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.16666667' to each side of the equation. -16.16666667 + 16.16666667 + x = 13.342705043 + 16.16666667 Combine like terms: -16.16666667 + 16.16666667 = 0.00000000 0.00000000 + x = 13.342705043 + 16.16666667 x = 13.342705043 + 16.16666667 Combine like terms: 13.342705043 + 16.16666667 = 29.509371713 x = 29.509371713 Simplifying x = 29.509371713Subproblem 2
x + -16.16666667 = -13.342705043 Simplifying x + -16.16666667 = -13.342705043 Reorder the terms: -16.16666667 + x = -13.342705043 Solving -16.16666667 + x = -13.342705043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.16666667' to each side of the equation. -16.16666667 + 16.16666667 + x = -13.342705043 + 16.16666667 Combine like terms: -16.16666667 + 16.16666667 = 0.00000000 0.00000000 + x = -13.342705043 + 16.16666667 x = -13.342705043 + 16.16666667 Combine like terms: -13.342705043 + 16.16666667 = 2.823961627 x = 2.823961627 Simplifying x = 2.823961627Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.509371713, 2.823961627}
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