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Simplifying 7x2 + -11x + -4 = 0 Reorder the terms: -4 + -11x + 7x2 = 0 Solving -4 + -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'. -0.5714285714 + -1.571428571x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -1.571428571x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -1.571428571x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -1.571428571x + x2 = 0 + 0.5714285714 -1.571428571x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -1.571428571x + x2 = 0.5714285714 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 = 0.5714285714 + 0.6173469384 Reorder the terms: 0.6173469384 + -1.571428571x + x2 = 0.5714285714 + 0.6173469384 Combine like terms: 0.5714285714 + 0.6173469384 = 1.1887755098 0.6173469384 + -1.571428571x + x2 = 1.1887755098 Factor a perfect square on the left side: (x + -0.7857142855)(x + -0.7857142855) = 1.1887755098 Calculate the square root of the right side: 1.090309823 Break this problem into two subproblems by setting (x + -0.7857142855) equal to 1.090309823 and -1.090309823.Subproblem 1
x + -0.7857142855 = 1.090309823 Simplifying x + -0.7857142855 = 1.090309823 Reorder the terms: -0.7857142855 + x = 1.090309823 Solving -0.7857142855 + x = 1.090309823 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 = 1.090309823 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = 1.090309823 + 0.7857142855 x = 1.090309823 + 0.7857142855 Combine like terms: 1.090309823 + 0.7857142855 = 1.8760241085 x = 1.8760241085 Simplifying x = 1.8760241085Subproblem 2
x + -0.7857142855 = -1.090309823 Simplifying x + -0.7857142855 = -1.090309823 Reorder the terms: -0.7857142855 + x = -1.090309823 Solving -0.7857142855 + x = -1.090309823 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 = -1.090309823 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = -1.090309823 + 0.7857142855 x = -1.090309823 + 0.7857142855 Combine like terms: -1.090309823 + 0.7857142855 = -0.3045955375 x = -0.3045955375 Simplifying x = -0.3045955375Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8760241085, -0.3045955375}
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