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Simplifying 7x2 + 40x + -25 = 0 Reorder the terms: -25 + 40x + 7x2 = 0 Solving -25 + 40x + 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'. -3.571428571 + 5.714285714x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + 5.714285714x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + 5.714285714x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + 5.714285714x + x2 = 0 + 3.571428571 5.714285714x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 5.714285714x + x2 = 3.571428571 The x term is 5.714285714x. Take half its coefficient (2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. 5.714285714x + 8.163265305 + x2 = 3.571428571 + 8.163265305 Reorder the terms: 8.163265305 + 5.714285714x + x2 = 3.571428571 + 8.163265305 Combine like terms: 3.571428571 + 8.163265305 = 11.734693876 8.163265305 + 5.714285714x + x2 = 11.734693876 Factor a perfect square on the left side: (x + 2.857142857)(x + 2.857142857) = 11.734693876 Calculate the square root of the right side: 3.425593945 Break this problem into two subproblems by setting (x + 2.857142857) equal to 3.425593945 and -3.425593945.Subproblem 1
x + 2.857142857 = 3.425593945 Simplifying x + 2.857142857 = 3.425593945 Reorder the terms: 2.857142857 + x = 3.425593945 Solving 2.857142857 + x = 3.425593945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = 3.425593945 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = 3.425593945 + -2.857142857 x = 3.425593945 + -2.857142857 Combine like terms: 3.425593945 + -2.857142857 = 0.568451088 x = 0.568451088 Simplifying x = 0.568451088Subproblem 2
x + 2.857142857 = -3.425593945 Simplifying x + 2.857142857 = -3.425593945 Reorder the terms: 2.857142857 + x = -3.425593945 Solving 2.857142857 + x = -3.425593945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = -3.425593945 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = -3.425593945 + -2.857142857 x = -3.425593945 + -2.857142857 Combine like terms: -3.425593945 + -2.857142857 = -6.282736802 x = -6.282736802 Simplifying x = -6.282736802Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.568451088, -6.282736802}
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