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Simplifying 21x + -1x2 + -30 = 0 Reorder the terms: -30 + 21x + -1x2 = 0 Solving -30 + 21x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -21x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -21x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -21x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -21x + x2 = 0 + -30 -21x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -21x + x2 = -30 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -30 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -30 + 110.25 Combine like terms: -30 + 110.25 = 80.25 110.25 + -21x + x2 = 80.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + -10.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + -10.5 = 8.958236434 Simplifying x + -10.5 = 8.958236434 Reorder the terms: -10.5 + x = 8.958236434 Solving -10.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 8.958236434 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 8.958236434 + 10.5 x = 8.958236434 + 10.5 Combine like terms: 8.958236434 + 10.5 = 19.458236434 x = 19.458236434 Simplifying x = 19.458236434Subproblem 2
x + -10.5 = -8.958236434 Simplifying x + -10.5 = -8.958236434 Reorder the terms: -10.5 + x = -8.958236434 Solving -10.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -8.958236434 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -8.958236434 + 10.5 x = -8.958236434 + 10.5 Combine like terms: -8.958236434 + 10.5 = 1.541763566 x = 1.541763566 Simplifying x = 1.541763566Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.458236434, 1.541763566}
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