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Simplifying 36x2 + 24x = 7 Reorder the terms: 24x + 36x2 = 7 Solving 24x + 36x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 24x + 36x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 24x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1944444444 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.1944444444' to each side of the equation. -0.1944444444 + 0.6666666667x + 0.1944444444 + x2 = 0 + 0.1944444444 Reorder the terms: -0.1944444444 + 0.1944444444 + 0.6666666667x + x2 = 0 + 0.1944444444 Combine like terms: -0.1944444444 + 0.1944444444 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + 0.1944444444 0.6666666667x + x2 = 0 + 0.1944444444 Combine like terms: 0 + 0.1944444444 = 0.1944444444 0.6666666667x + x2 = 0.1944444444 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.1944444444 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.1944444444 + 0.1111111112 Combine like terms: 0.1944444444 + 0.1111111112 = 0.3055555556 0.1111111112 + 0.6666666667x + x2 = 0.3055555556 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.3055555556 Calculate the square root of the right side: 0.552770798 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.552770798 and -0.552770798.Subproblem 1
x + 0.3333333334 = 0.552770798 Simplifying x + 0.3333333334 = 0.552770798 Reorder the terms: 0.3333333334 + x = 0.552770798 Solving 0.3333333334 + x = 0.552770798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.552770798 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.552770798 + -0.3333333334 x = 0.552770798 + -0.3333333334 Combine like terms: 0.552770798 + -0.3333333334 = 0.2194374646 x = 0.2194374646 Simplifying x = 0.2194374646Subproblem 2
x + 0.3333333334 = -0.552770798 Simplifying x + 0.3333333334 = -0.552770798 Reorder the terms: 0.3333333334 + x = -0.552770798 Solving 0.3333333334 + x = -0.552770798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.552770798 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.552770798 + -0.3333333334 x = -0.552770798 + -0.3333333334 Combine like terms: -0.552770798 + -0.3333333334 = -0.8861041314 x = -0.8861041314 Simplifying x = -0.8861041314Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2194374646, -0.8861041314}
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