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Simplifying 1.75x2 + 30x + -100 = 0 Reorder the terms: -100 + 30x + 1.75x2 = 0 Solving -100 + 30x + 1.75x2 = 0 Solving for variable 'x'. 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 = 130.61224487 73.46938773 + 17.14285714x + x2 = 130.61224487 Factor a perfect square on the left side: (x + 8.57142857)(x + 8.57142857) = 130.61224487 Calculate the square root of the right side: 11.428571427 Break this problem into two subproblems by setting (x + 8.57142857) equal to 11.428571427 and -11.428571427.Subproblem 1
x + 8.57142857 = 11.428571427 Simplifying x + 8.57142857 = 11.428571427 Reorder the terms: 8.57142857 + x = 11.428571427 Solving 8.57142857 + x = 11.428571427 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 = 11.428571427 + -8.57142857 Combine like terms: 8.57142857 + -8.57142857 = 0.00000000 0.00000000 + x = 11.428571427 + -8.57142857 x = 11.428571427 + -8.57142857 Combine like terms: 11.428571427 + -8.57142857 = 2.857142857 x = 2.857142857 Simplifying x = 2.857142857Subproblem 2
x + 8.57142857 = -11.428571427 Simplifying x + 8.57142857 = -11.428571427 Reorder the terms: 8.57142857 + x = -11.428571427 Solving 8.57142857 + x = -11.428571427 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 = -11.428571427 + -8.57142857 Combine like terms: 8.57142857 + -8.57142857 = 0.00000000 0.00000000 + x = -11.428571427 + -8.57142857 x = -11.428571427 + -8.57142857 Combine like terms: -11.428571427 + -8.57142857 = -19.999999997 x = -19.999999997 Simplifying x = -19.999999997Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.857142857, -19.999999997}
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