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Simplifying 7x2 + 31x + 4 = 0 Reorder the terms: 4 + 31x + 7x2 = 0 Solving 4 + 31x + 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 + 4.428571429x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + 4.428571429x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + 4.428571429x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + 4.428571429x + x2 = 0 + -0.5714285714 4.428571429x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 4.428571429x + x2 = -0.5714285714 The x term is 4.428571429x. Take half its coefficient (2.214285715). Square it (4.903061228) and add it to both sides. Add '4.903061228' to each side of the equation. 4.428571429x + 4.903061228 + x2 = -0.5714285714 + 4.903061228 Reorder the terms: 4.903061228 + 4.428571429x + x2 = -0.5714285714 + 4.903061228 Combine like terms: -0.5714285714 + 4.903061228 = 4.3316326566 4.903061228 + 4.428571429x + x2 = 4.3316326566 Factor a perfect square on the left side: (x + 2.214285715)(x + 2.214285715) = 4.3316326566 Calculate the square root of the right side: 2.08125747 Break this problem into two subproblems by setting (x + 2.214285715) equal to 2.08125747 and -2.08125747.Subproblem 1
x + 2.214285715 = 2.08125747 Simplifying x + 2.214285715 = 2.08125747 Reorder the terms: 2.214285715 + x = 2.08125747 Solving 2.214285715 + x = 2.08125747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.214285715' to each side of the equation. 2.214285715 + -2.214285715 + x = 2.08125747 + -2.214285715 Combine like terms: 2.214285715 + -2.214285715 = 0.000000000 0.000000000 + x = 2.08125747 + -2.214285715 x = 2.08125747 + -2.214285715 Combine like terms: 2.08125747 + -2.214285715 = -0.133028245 x = -0.133028245 Simplifying x = -0.133028245Subproblem 2
x + 2.214285715 = -2.08125747 Simplifying x + 2.214285715 = -2.08125747 Reorder the terms: 2.214285715 + x = -2.08125747 Solving 2.214285715 + x = -2.08125747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.214285715' to each side of the equation. 2.214285715 + -2.214285715 + x = -2.08125747 + -2.214285715 Combine like terms: 2.214285715 + -2.214285715 = 0.000000000 0.000000000 + x = -2.08125747 + -2.214285715 x = -2.08125747 + -2.214285715 Combine like terms: -2.08125747 + -2.214285715 = -4.295543185 x = -4.295543185 Simplifying x = -4.295543185Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.133028245, -4.295543185}
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