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Simplifying 7x2 + 11x + -8 = 0 Reorder the terms: -8 + 11x + 7x2 = 0 Solving -8 + 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'. -1.142857143 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 1.571428571x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 1.571428571x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 1.571428571x + x2 = 0 + 1.142857143 1.571428571x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 1.571428571x + x2 = 1.142857143 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 = 1.142857143 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = 1.142857143 + 0.6173469384 Combine like terms: 1.142857143 + 0.6173469384 = 1.7602040814 0.6173469384 + 1.571428571x + x2 = 1.7602040814 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 1.7602040814 Calculate the square root of the right side: 1.32672683 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 1.32672683 and -1.32672683.Subproblem 1
x + 0.7857142855 = 1.32672683 Simplifying x + 0.7857142855 = 1.32672683 Reorder the terms: 0.7857142855 + x = 1.32672683 Solving 0.7857142855 + x = 1.32672683 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 = 1.32672683 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 1.32672683 + -0.7857142855 x = 1.32672683 + -0.7857142855 Combine like terms: 1.32672683 + -0.7857142855 = 0.5410125445 x = 0.5410125445 Simplifying x = 0.5410125445Subproblem 2
x + 0.7857142855 = -1.32672683 Simplifying x + 0.7857142855 = -1.32672683 Reorder the terms: 0.7857142855 + x = -1.32672683 Solving 0.7857142855 + x = -1.32672683 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 = -1.32672683 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -1.32672683 + -0.7857142855 x = -1.32672683 + -0.7857142855 Combine like terms: -1.32672683 + -0.7857142855 = -2.1124411155 x = -2.1124411155 Simplifying x = -2.1124411155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5410125445, -2.1124411155}
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