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Simplifying 21x2 + 150x = 1000 Reorder the terms: 150x + 21x2 = 1000 Solving 150x + 21x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + 150x + 21x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 150x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -47.61904762 + 7.142857143x + x2 = 0 Move the constant term to the right: Add '47.61904762' to each side of the equation. -47.61904762 + 7.142857143x + 47.61904762 + x2 = 0 + 47.61904762 Reorder the terms: -47.61904762 + 47.61904762 + 7.142857143x + x2 = 0 + 47.61904762 Combine like terms: -47.61904762 + 47.61904762 = 0.00000000 0.00000000 + 7.142857143x + x2 = 0 + 47.61904762 7.142857143x + x2 = 0 + 47.61904762 Combine like terms: 0 + 47.61904762 = 47.61904762 7.142857143x + x2 = 47.61904762 The x term is 7.142857143x. Take half its coefficient (3.571428572). Square it (12.75510204) and add it to both sides. Add '12.75510204' to each side of the equation. 7.142857143x + 12.75510204 + x2 = 47.61904762 + 12.75510204 Reorder the terms: 12.75510204 + 7.142857143x + x2 = 47.61904762 + 12.75510204 Combine like terms: 47.61904762 + 12.75510204 = 60.37414966 12.75510204 + 7.142857143x + x2 = 60.37414966 Factor a perfect square on the left side: (x + 3.571428572)(x + 3.571428572) = 60.37414966 Calculate the square root of the right side: 7.770080415 Break this problem into two subproblems by setting (x + 3.571428572) equal to 7.770080415 and -7.770080415.Subproblem 1
x + 3.571428572 = 7.770080415 Simplifying x + 3.571428572 = 7.770080415 Reorder the terms: 3.571428572 + x = 7.770080415 Solving 3.571428572 + x = 7.770080415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + x = 7.770080415 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + x = 7.770080415 + -3.571428572 x = 7.770080415 + -3.571428572 Combine like terms: 7.770080415 + -3.571428572 = 4.198651843 x = 4.198651843 Simplifying x = 4.198651843Subproblem 2
x + 3.571428572 = -7.770080415 Simplifying x + 3.571428572 = -7.770080415 Reorder the terms: 3.571428572 + x = -7.770080415 Solving 3.571428572 + x = -7.770080415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + x = -7.770080415 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + x = -7.770080415 + -3.571428572 x = -7.770080415 + -3.571428572 Combine like terms: -7.770080415 + -3.571428572 = -11.341508987 x = -11.341508987 Simplifying x = -11.341508987Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.198651843, -11.341508987}
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