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Simplifying -0.095x2 + 1.74x + 60 = 36 Reorder the terms: 60 + 1.74x + -0.095x2 = 36 Solving 60 + 1.74x + -0.095x2 = 36 Solving for variable 'x'. Reorder the terms: 60 + -36 + 1.74x + -0.095x2 = 36 + -36 Combine like terms: 60 + -36 = 24 24 + 1.74x + -0.095x2 = 36 + -36 Combine like terms: 36 + -36 = 0 24 + 1.74x + -0.095x2 = 0 Begin completing the square. Divide all terms by -0.095 the coefficient of the squared term: Divide each side by '-0.095'. -252.6315789 + -18.31578947x + x2 = 0 Move the constant term to the right: Add '252.6315789' to each side of the equation. -252.6315789 + -18.31578947x + 252.6315789 + x2 = 0 + 252.6315789 Reorder the terms: -252.6315789 + 252.6315789 + -18.31578947x + x2 = 0 + 252.6315789 Combine like terms: -252.6315789 + 252.6315789 = 0.0000000 0.0000000 + -18.31578947x + x2 = 0 + 252.6315789 -18.31578947x + x2 = 0 + 252.6315789 Combine like terms: 0 + 252.6315789 = 252.6315789 -18.31578947x + x2 = 252.6315789 The x term is -18.31578947x. Take half its coefficient (-9.157894735). Square it (83.86703598) and add it to both sides. Add '83.86703598' to each side of the equation. -18.31578947x + 83.86703598 + x2 = 252.6315789 + 83.86703598 Reorder the terms: 83.86703598 + -18.31578947x + x2 = 252.6315789 + 83.86703598 Combine like terms: 252.6315789 + 83.86703598 = 336.49861488 83.86703598 + -18.31578947x + x2 = 336.49861488 Factor a perfect square on the left side: (x + -9.157894735)(x + -9.157894735) = 336.49861488 Calculate the square root of the right side: 18.343898574 Break this problem into two subproblems by setting (x + -9.157894735) equal to 18.343898574 and -18.343898574.Subproblem 1
x + -9.157894735 = 18.343898574 Simplifying x + -9.157894735 = 18.343898574 Reorder the terms: -9.157894735 + x = 18.343898574 Solving -9.157894735 + x = 18.343898574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.157894735' to each side of the equation. -9.157894735 + 9.157894735 + x = 18.343898574 + 9.157894735 Combine like terms: -9.157894735 + 9.157894735 = 0.000000000 0.000000000 + x = 18.343898574 + 9.157894735 x = 18.343898574 + 9.157894735 Combine like terms: 18.343898574 + 9.157894735 = 27.501793309 x = 27.501793309 Simplifying x = 27.501793309Subproblem 2
x + -9.157894735 = -18.343898574 Simplifying x + -9.157894735 = -18.343898574 Reorder the terms: -9.157894735 + x = -18.343898574 Solving -9.157894735 + x = -18.343898574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.157894735' to each side of the equation. -9.157894735 + 9.157894735 + x = -18.343898574 + 9.157894735 Combine like terms: -9.157894735 + 9.157894735 = 0.000000000 0.000000000 + x = -18.343898574 + 9.157894735 x = -18.343898574 + 9.157894735 Combine like terms: -18.343898574 + 9.157894735 = -9.186003839 x = -9.186003839 Simplifying x = -9.186003839Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.501793309, -9.186003839}
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