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Simplifying x(3x + -10) = 90 Reorder the terms: x(-10 + 3x) = 90 (-10 * x + 3x * x) = 90 (-10x + 3x2) = 90 Solving -10x + 3x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -10x + 3x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -3.333333333x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -3.333333333x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -3.333333333x + x2 = 0 + 30 -3.333333333x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -3.333333333x + x2 = 30 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 30 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 30 + 2.777777779 Combine like terms: 30 + 2.777777779 = 32.777777779 2.777777779 + -3.333333333x + x2 = 32.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 32.777777779 Calculate the square root of the right side: 5.725188013 Break this problem into two subproblems by setting (x + -1.666666667) equal to 5.725188013 and -5.725188013.Subproblem 1
x + -1.666666667 = 5.725188013 Simplifying x + -1.666666667 = 5.725188013 Reorder the terms: -1.666666667 + x = 5.725188013 Solving -1.666666667 + x = 5.725188013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 5.725188013 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 5.725188013 + 1.666666667 x = 5.725188013 + 1.666666667 Combine like terms: 5.725188013 + 1.666666667 = 7.39185468 x = 7.39185468 Simplifying x = 7.39185468Subproblem 2
x + -1.666666667 = -5.725188013 Simplifying x + -1.666666667 = -5.725188013 Reorder the terms: -1.666666667 + x = -5.725188013 Solving -1.666666667 + x = -5.725188013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -5.725188013 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -5.725188013 + 1.666666667 x = -5.725188013 + 1.666666667 Combine like terms: -5.725188013 + 1.666666667 = -4.058521346 x = -4.058521346 Simplifying x = -4.058521346Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.39185468, -4.058521346}
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