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Simplifying x(3x + -790) = -18900 Reorder the terms: x(-790 + 3x) = -18900 (-790 * x + 3x * x) = -18900 (-790x + 3x2) = -18900 Solving -790x + 3x2 = -18900 Solving for variable 'x'. Reorder the terms: 18900 + -790x + 3x2 = -18900 + 18900 Combine like terms: -18900 + 18900 = 0 18900 + -790x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6300 + -263.3333333x + x2 = 0 Move the constant term to the right: Add '-6300' to each side of the equation. 6300 + -263.3333333x + -6300 + x2 = 0 + -6300 Reorder the terms: 6300 + -6300 + -263.3333333x + x2 = 0 + -6300 Combine like terms: 6300 + -6300 = 0 0 + -263.3333333x + x2 = 0 + -6300 -263.3333333x + x2 = 0 + -6300 Combine like terms: 0 + -6300 = -6300 -263.3333333x + x2 = -6300 The x term is -263.3333333x. Take half its coefficient (-131.6666667). Square it (17336.11112) and add it to both sides. Add '17336.11112' to each side of the equation. -263.3333333x + 17336.11112 + x2 = -6300 + 17336.11112 Reorder the terms: 17336.11112 + -263.3333333x + x2 = -6300 + 17336.11112 Combine like terms: -6300 + 17336.11112 = 11036.11112 17336.11112 + -263.3333333x + x2 = 11036.11112 Factor a perfect square on the left side: (x + -131.6666667)(x + -131.6666667) = 11036.11112 Calculate the square root of the right side: 105.052896771 Break this problem into two subproblems by setting (x + -131.6666667) equal to 105.052896771 and -105.052896771.Subproblem 1
x + -131.6666667 = 105.052896771 Simplifying x + -131.6666667 = 105.052896771 Reorder the terms: -131.6666667 + x = 105.052896771 Solving -131.6666667 + x = 105.052896771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '131.6666667' to each side of the equation. -131.6666667 + 131.6666667 + x = 105.052896771 + 131.6666667 Combine like terms: -131.6666667 + 131.6666667 = 0.0000000 0.0000000 + x = 105.052896771 + 131.6666667 x = 105.052896771 + 131.6666667 Combine like terms: 105.052896771 + 131.6666667 = 236.719563471 x = 236.719563471 Simplifying x = 236.719563471Subproblem 2
x + -131.6666667 = -105.052896771 Simplifying x + -131.6666667 = -105.052896771 Reorder the terms: -131.6666667 + x = -105.052896771 Solving -131.6666667 + x = -105.052896771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '131.6666667' to each side of the equation. -131.6666667 + 131.6666667 + x = -105.052896771 + 131.6666667 Combine like terms: -131.6666667 + 131.6666667 = 0.0000000 0.0000000 + x = -105.052896771 + 131.6666667 x = -105.052896771 + 131.6666667 Combine like terms: -105.052896771 + 131.6666667 = 26.613769929 x = 26.613769929 Simplifying x = 26.613769929Solution
The solution to the problem is based on the solutions from the subproblems. x = {236.719563471, 26.613769929}
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