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Simplifying 7x2 + 11x + -84 = 0 Reorder the terms: -84 + 11x + 7x2 = 0 Solving -84 + 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'. -12 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 1.571428571x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 1.571428571x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 1.571428571x + x2 = 0 + 12 1.571428571x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 1.571428571x + x2 = 12 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 = 12 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = 12 + 0.6173469384 Combine like terms: 12 + 0.6173469384 = 12.6173469384 0.6173469384 + 1.571428571x + x2 = 12.6173469384 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 12.6173469384 Calculate the square root of the right side: 3.552090503 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 3.552090503 and -3.552090503.Subproblem 1
x + 0.7857142855 = 3.552090503 Simplifying x + 0.7857142855 = 3.552090503 Reorder the terms: 0.7857142855 + x = 3.552090503 Solving 0.7857142855 + x = 3.552090503 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 = 3.552090503 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 3.552090503 + -0.7857142855 x = 3.552090503 + -0.7857142855 Combine like terms: 3.552090503 + -0.7857142855 = 2.7663762175 x = 2.7663762175 Simplifying x = 2.7663762175Subproblem 2
x + 0.7857142855 = -3.552090503 Simplifying x + 0.7857142855 = -3.552090503 Reorder the terms: 0.7857142855 + x = -3.552090503 Solving 0.7857142855 + x = -3.552090503 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 = -3.552090503 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -3.552090503 + -0.7857142855 x = -3.552090503 + -0.7857142855 Combine like terms: -3.552090503 + -0.7857142855 = -4.3378047885 x = -4.3378047885 Simplifying x = -4.3378047885Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7663762175, -4.3378047885}
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