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Simplifying 20x2 + 40x = 7 Reorder the terms: 40x + 20x2 = 7 Solving 40x + 20x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 40x + 20x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 40x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.35 + 2x + x2 = 0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + 2x + 0.35 + x2 = 0 + 0.35 Reorder the terms: -0.35 + 0.35 + 2x + x2 = 0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + 2x + x2 = 0 + 0.35 2x + x2 = 0 + 0.35 Combine like terms: 0 + 0.35 = 0.35 2x + x2 = 0.35 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.35 + 1 Reorder the terms: 1 + 2x + x2 = 0.35 + 1 Combine like terms: 0.35 + 1 = 1.35 1 + 2x + x2 = 1.35 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.35 Calculate the square root of the right side: 1.161895004 Break this problem into two subproblems by setting (x + 1) equal to 1.161895004 and -1.161895004.Subproblem 1
x + 1 = 1.161895004 Simplifying x + 1 = 1.161895004 Reorder the terms: 1 + x = 1.161895004 Solving 1 + x = 1.161895004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.161895004 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.161895004 + -1 x = 1.161895004 + -1 Combine like terms: 1.161895004 + -1 = 0.161895004 x = 0.161895004 Simplifying x = 0.161895004Subproblem 2
x + 1 = -1.161895004 Simplifying x + 1 = -1.161895004 Reorder the terms: 1 + x = -1.161895004 Solving 1 + x = -1.161895004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.161895004 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.161895004 + -1 x = -1.161895004 + -1 Combine like terms: -1.161895004 + -1 = -2.161895004 x = -2.161895004 Simplifying x = -2.161895004Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.161895004, -2.161895004}
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