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Simplifying 30x + -1.75x2 = 100 Solving 30x + -1.75x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 30x + -1.75x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 30x + -1.75x2 = 0 Begin completing the square. Divide all terms by -1.75 the coefficient of the squared term: Divide each side by '-1.75'. 57.14285714 + -17.14285714x + x2 = 0 Move the constant term to the right: Add '-57.14285714' to each side of the equation. 57.14285714 + -17.14285714x + -57.14285714 + x2 = 0 + -57.14285714 Reorder the terms: 57.14285714 + -57.14285714 + -17.14285714x + x2 = 0 + -57.14285714 Combine like terms: 57.14285714 + -57.14285714 = 0.00000000 0.00000000 + -17.14285714x + x2 = 0 + -57.14285714 -17.14285714x + x2 = 0 + -57.14285714 Combine like terms: 0 + -57.14285714 = -57.14285714 -17.14285714x + x2 = -57.14285714 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 = -57.14285714 + 73.46938773 Reorder the terms: 73.46938773 + -17.14285714x + x2 = -57.14285714 + 73.46938773 Combine like terms: -57.14285714 + 73.46938773 = 16.32653059 73.46938773 + -17.14285714x + x2 = 16.32653059 Factor a perfect square on the left side: (x + -8.57142857)(x + -8.57142857) = 16.32653059 Calculate the square root of the right side: 4.040610175 Break this problem into two subproblems by setting (x + -8.57142857) equal to 4.040610175 and -4.040610175.Subproblem 1
x + -8.57142857 = 4.040610175 Simplifying x + -8.57142857 = 4.040610175 Reorder the terms: -8.57142857 + x = 4.040610175 Solving -8.57142857 + x = 4.040610175 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 = 4.040610175 + 8.57142857 Combine like terms: -8.57142857 + 8.57142857 = 0.00000000 0.00000000 + x = 4.040610175 + 8.57142857 x = 4.040610175 + 8.57142857 Combine like terms: 4.040610175 + 8.57142857 = 12.612038745 x = 12.612038745 Simplifying x = 12.612038745Subproblem 2
x + -8.57142857 = -4.040610175 Simplifying x + -8.57142857 = -4.040610175 Reorder the terms: -8.57142857 + x = -4.040610175 Solving -8.57142857 + x = -4.040610175 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 = -4.040610175 + 8.57142857 Combine like terms: -8.57142857 + 8.57142857 = 0.00000000 0.00000000 + x = -4.040610175 + 8.57142857 x = -4.040610175 + 8.57142857 Combine like terms: -4.040610175 + 8.57142857 = 4.530818395 x = 4.530818395 Simplifying x = 4.530818395Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.612038745, 4.530818395}
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