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Simplifying 7x2 + 11x + -21 = 0 Reorder the terms: -21 + 11x + 7x2 = 0 Solving -21 + 11x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.571428571x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.571428571x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.571428571x + x2 = 0 + 3 1.571428571x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.571428571x + x2 = 3 The x term is 1.571428571x. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x + 0.6173469384 + x2 = 3 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = 3 + 0.6173469384 Combine like terms: 3 + 0.6173469384 = 3.6173469384 0.6173469384 + 1.571428571x + x2 = 3.6173469384 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 3.6173469384 Calculate the square root of the right side: 1.901932422 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 1.901932422 and -1.901932422.Subproblem 1
x + 0.7857142855 = 1.901932422 Simplifying x + 0.7857142855 = 1.901932422 Reorder the terms: 0.7857142855 + x = 1.901932422 Solving 0.7857142855 + x = 1.901932422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 1.901932422 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 1.901932422 + -0.7857142855 x = 1.901932422 + -0.7857142855 Combine like terms: 1.901932422 + -0.7857142855 = 1.1162181365 x = 1.1162181365 Simplifying x = 1.1162181365Subproblem 2
x + 0.7857142855 = -1.901932422 Simplifying x + 0.7857142855 = -1.901932422 Reorder the terms: 0.7857142855 + x = -1.901932422 Solving 0.7857142855 + x = -1.901932422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -1.901932422 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -1.901932422 + -0.7857142855 x = -1.901932422 + -0.7857142855 Combine like terms: -1.901932422 + -0.7857142855 = -2.6876467075 x = -2.6876467075 Simplifying x = -2.6876467075Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1162181365, -2.6876467075}
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