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Simplifying x(0.21x + -10) = 25 Reorder the terms: x(-10 + 0.21x) = 25 (-10 * x + 0.21x * x) = 25 (-10x + 0.21x2) = 25 Solving -10x + 0.21x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -10x + 0.21x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -10x + 0.21x2 = 0 Begin completing the square. Divide all terms by 0.21 the coefficient of the squared term: Divide each side by '0.21'. -119.047619 + -47.61904762x + x2 = 0 Move the constant term to the right: Add '119.047619' to each side of the equation. -119.047619 + -47.61904762x + 119.047619 + x2 = 0 + 119.047619 Reorder the terms: -119.047619 + 119.047619 + -47.61904762x + x2 = 0 + 119.047619 Combine like terms: -119.047619 + 119.047619 = 0.000000 0.000000 + -47.61904762x + x2 = 0 + 119.047619 -47.61904762x + x2 = 0 + 119.047619 Combine like terms: 0 + 119.047619 = 119.047619 -47.61904762x + x2 = 119.047619 The x term is -47.61904762x. Take half its coefficient (-23.80952381). Square it (566.8934241) and add it to both sides. Add '566.8934241' to each side of the equation. -47.61904762x + 566.8934241 + x2 = 119.047619 + 566.8934241 Reorder the terms: 566.8934241 + -47.61904762x + x2 = 119.047619 + 566.8934241 Combine like terms: 119.047619 + 566.8934241 = 685.9410431 566.8934241 + -47.61904762x + x2 = 685.9410431 Factor a perfect square on the left side: (x + -23.80952381)(x + -23.80952381) = 685.9410431 Calculate the square root of the right side: 26.190476191 Break this problem into two subproblems by setting (x + -23.80952381) equal to 26.190476191 and -26.190476191.Subproblem 1
x + -23.80952381 = 26.190476191 Simplifying x + -23.80952381 = 26.190476191 Reorder the terms: -23.80952381 + x = 26.190476191 Solving -23.80952381 + x = 26.190476191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.80952381' to each side of the equation. -23.80952381 + 23.80952381 + x = 26.190476191 + 23.80952381 Combine like terms: -23.80952381 + 23.80952381 = 0.00000000 0.00000000 + x = 26.190476191 + 23.80952381 x = 26.190476191 + 23.80952381 Combine like terms: 26.190476191 + 23.80952381 = 50.000000001 x = 50.000000001 Simplifying x = 50.000000001Subproblem 2
x + -23.80952381 = -26.190476191 Simplifying x + -23.80952381 = -26.190476191 Reorder the terms: -23.80952381 + x = -26.190476191 Solving -23.80952381 + x = -26.190476191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.80952381' to each side of the equation. -23.80952381 + 23.80952381 + x = -26.190476191 + 23.80952381 Combine like terms: -23.80952381 + 23.80952381 = 0.00000000 0.00000000 + x = -26.190476191 + 23.80952381 x = -26.190476191 + 23.80952381 Combine like terms: -26.190476191 + 23.80952381 = -2.380952381 x = -2.380952381 Simplifying x = -2.380952381Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.000000001, -2.380952381}
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