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Simplifying (3x2 + -21x) = 26 Reorder the terms: (-21x + 3x2) = 26 Remove parenthesis around (-21x + 3x2) -21x + 3x2 = 26 Solving -21x + 3x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -21x + 3x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.666666667 + -7x + x2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + -7x + 8.666666667 + x2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + -7x + x2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + -7x + x2 = 0 + 8.666666667 -7x + x2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 -7x + x2 = 8.666666667 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 8.666666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 8.666666667 + 12.25 Combine like terms: 8.666666667 + 12.25 = 20.916666667 12.25 + -7x + x2 = 20.916666667 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 20.916666667 Calculate the square root of the right side: 4.573474245 Break this problem into two subproblems by setting (x + -3.5) equal to 4.573474245 and -4.573474245.Subproblem 1
x + -3.5 = 4.573474245 Simplifying x + -3.5 = 4.573474245 Reorder the terms: -3.5 + x = 4.573474245 Solving -3.5 + x = 4.573474245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.573474245 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.573474245 + 3.5 x = 4.573474245 + 3.5 Combine like terms: 4.573474245 + 3.5 = 8.073474245 x = 8.073474245 Simplifying x = 8.073474245Subproblem 2
x + -3.5 = -4.573474245 Simplifying x + -3.5 = -4.573474245 Reorder the terms: -3.5 + x = -4.573474245 Solving -3.5 + x = -4.573474245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.573474245 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.573474245 + 3.5 x = -4.573474245 + 3.5 Combine like terms: -4.573474245 + 3.5 = -1.073474245 x = -1.073474245 Simplifying x = -1.073474245Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.073474245, -1.073474245}
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