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Simplifying 36x2 + -24x = 146 Reorder the terms: -24x + 36x2 = 146 Solving -24x + 36x2 = 146 Solving for variable 'x'. Reorder the terms: -146 + -24x + 36x2 = 146 + -146 Combine like terms: 146 + -146 = 0 -146 + -24x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-73 + -12x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-73 + -12x + 18x2)' equal to zero and attempt to solve: Simplifying -73 + -12x + 18x2 = 0 Solving -73 + -12x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -4.055555556 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '4.055555556' to each side of the equation. -4.055555556 + -0.6666666667x + 4.055555556 + x2 = 0 + 4.055555556 Reorder the terms: -4.055555556 + 4.055555556 + -0.6666666667x + x2 = 0 + 4.055555556 Combine like terms: -4.055555556 + 4.055555556 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + 4.055555556 -0.6666666667x + x2 = 0 + 4.055555556 Combine like terms: 0 + 4.055555556 = 4.055555556 -0.6666666667x + x2 = 4.055555556 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 = 4.055555556 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 4.055555556 + 0.1111111112 Combine like terms: 4.055555556 + 0.1111111112 = 4.1666666672 0.1111111112 + -0.6666666667x + x2 = 4.1666666672 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 4.1666666672 Calculate the square root of the right side: 2.041241452 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 2.041241452 and -2.041241452.Subproblem 1
x + -0.3333333334 = 2.041241452 Simplifying x + -0.3333333334 = 2.041241452 Reorder the terms: -0.3333333334 + x = 2.041241452 Solving -0.3333333334 + x = 2.041241452 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 = 2.041241452 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.041241452 + 0.3333333334 x = 2.041241452 + 0.3333333334 Combine like terms: 2.041241452 + 0.3333333334 = 2.3745747854 x = 2.3745747854 Simplifying x = 2.3745747854Subproblem 2
x + -0.3333333334 = -2.041241452 Simplifying x + -0.3333333334 = -2.041241452 Reorder the terms: -0.3333333334 + x = -2.041241452 Solving -0.3333333334 + x = -2.041241452 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 = -2.041241452 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.041241452 + 0.3333333334 x = -2.041241452 + 0.3333333334 Combine like terms: -2.041241452 + 0.3333333334 = -1.7079081186 x = -1.7079081186 Simplifying x = -1.7079081186Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3745747854, -1.7079081186}Solution
x = {2.3745747854, -1.7079081186}
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