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Simplifying 30700 = -36x2 + 1440x + 19224 Reorder the terms: 30700 = 19224 + 1440x + -36x2 Solving 30700 = 19224 + 1440x + -36x2 Solving for variable 'x'. Combine like terms: 30700 + -19224 = 11476 11476 + -1440x + 36x2 = 19224 + 1440x + -36x2 + -19224 + -1440x + 36x2 Reorder the terms: 11476 + -1440x + 36x2 = 19224 + -19224 + 1440x + -1440x + -36x2 + 36x2 Combine like terms: 19224 + -19224 = 0 11476 + -1440x + 36x2 = 0 + 1440x + -1440x + -36x2 + 36x2 11476 + -1440x + 36x2 = 1440x + -1440x + -36x2 + 36x2 Combine like terms: 1440x + -1440x = 0 11476 + -1440x + 36x2 = 0 + -36x2 + 36x2 11476 + -1440x + 36x2 = -36x2 + 36x2 Combine like terms: -36x2 + 36x2 = 0 11476 + -1440x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2869 + -360x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2869 + -360x + 9x2)' equal to zero and attempt to solve: Simplifying 2869 + -360x + 9x2 = 0 Solving 2869 + -360x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 318.7777778 + -40x + x2 = 0 Move the constant term to the right: Add '-318.7777778' to each side of the equation. 318.7777778 + -40x + -318.7777778 + x2 = 0 + -318.7777778 Reorder the terms: 318.7777778 + -318.7777778 + -40x + x2 = 0 + -318.7777778 Combine like terms: 318.7777778 + -318.7777778 = 0.0000000 0.0000000 + -40x + x2 = 0 + -318.7777778 -40x + x2 = 0 + -318.7777778 Combine like terms: 0 + -318.7777778 = -318.7777778 -40x + x2 = -318.7777778 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -318.7777778 + 400 Reorder the terms: 400 + -40x + x2 = -318.7777778 + 400 Combine like terms: -318.7777778 + 400 = 81.2222222 400 + -40x + x2 = 81.2222222 Factor a perfect square on the left side: (x + -20)(x + -20) = 81.2222222 Calculate the square root of the right side: 9.012337222 Break this problem into two subproblems by setting (x + -20) equal to 9.012337222 and -9.012337222.Subproblem 1
x + -20 = 9.012337222 Simplifying x + -20 = 9.012337222 Reorder the terms: -20 + x = 9.012337222 Solving -20 + x = 9.012337222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 9.012337222 + 20 Combine like terms: -20 + 20 = 0 0 + x = 9.012337222 + 20 x = 9.012337222 + 20 Combine like terms: 9.012337222 + 20 = 29.012337222 x = 29.012337222 Simplifying x = 29.012337222Subproblem 2
x + -20 = -9.012337222 Simplifying x + -20 = -9.012337222 Reorder the terms: -20 + x = -9.012337222 Solving -20 + x = -9.012337222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -9.012337222 + 20 Combine like terms: -20 + 20 = 0 0 + x = -9.012337222 + 20 x = -9.012337222 + 20 Combine like terms: -9.012337222 + 20 = 10.987662778 x = 10.987662778 Simplifying x = 10.987662778Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.012337222, 10.987662778}Solution
x = {29.012337222, 10.987662778}
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