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Simplifying 5x2 + -40x = 2 Reorder the terms: -40x + 5x2 = 2 Solving -40x + 5x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -40x + 5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -8x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -8x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -8x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -8x + x2 = 0 + 0.4 -8x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -8x + x2 = 0.4 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 0.4 + 16 Reorder the terms: 16 + -8x + x2 = 0.4 + 16 Combine like terms: 0.4 + 16 = 16.4 16 + -8x + x2 = 16.4 Factor a perfect square on the left side: (x + -4)(x + -4) = 16.4 Calculate the square root of the right side: 4.049691346 Break this problem into two subproblems by setting (x + -4) equal to 4.049691346 and -4.049691346.Subproblem 1
x + -4 = 4.049691346 Simplifying x + -4 = 4.049691346 Reorder the terms: -4 + x = 4.049691346 Solving -4 + x = 4.049691346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.049691346 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.049691346 + 4 x = 4.049691346 + 4 Combine like terms: 4.049691346 + 4 = 8.049691346 x = 8.049691346 Simplifying x = 8.049691346Subproblem 2
x + -4 = -4.049691346 Simplifying x + -4 = -4.049691346 Reorder the terms: -4 + x = -4.049691346 Solving -4 + x = -4.049691346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.049691346 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.049691346 + 4 x = -4.049691346 + 4 Combine like terms: -4.049691346 + 4 = -0.049691346 x = -0.049691346 Simplifying x = -0.049691346Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.049691346, -0.049691346}
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