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Simplifying 5x2 = 40x + 16 Reorder the terms: 5x2 = 16 + 40x Solving 5x2 = 16 + 40x Solving for variable 'x'. Reorder the terms: -16 + -40x + 5x2 = 16 + 40x + -16 + -40x Reorder the terms: -16 + -40x + 5x2 = 16 + -16 + 40x + -40x Combine like terms: 16 + -16 = 0 -16 + -40x + 5x2 = 0 + 40x + -40x -16 + -40x + 5x2 = 40x + -40x Combine like terms: 40x + -40x = 0 -16 + -40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -8x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -8x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -8x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -8x + x2 = 0 + 3.2 -8x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -8x + x2 = 3.2 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 = 3.2 + 16 Reorder the terms: 16 + -8x + x2 = 3.2 + 16 Combine like terms: 3.2 + 16 = 19.2 16 + -8x + x2 = 19.2 Factor a perfect square on the left side: (x + -4)(x + -4) = 19.2 Calculate the square root of the right side: 4.38178046 Break this problem into two subproblems by setting (x + -4) equal to 4.38178046 and -4.38178046.Subproblem 1
x + -4 = 4.38178046 Simplifying x + -4 = 4.38178046 Reorder the terms: -4 + x = 4.38178046 Solving -4 + x = 4.38178046 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 = 4.38178046 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.38178046 + 4 x = 4.38178046 + 4 Combine like terms: 4.38178046 + 4 = 8.38178046 x = 8.38178046 Simplifying x = 8.38178046Subproblem 2
x + -4 = -4.38178046 Simplifying x + -4 = -4.38178046 Reorder the terms: -4 + x = -4.38178046 Solving -4 + x = -4.38178046 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 = -4.38178046 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.38178046 + 4 x = -4.38178046 + 4 Combine like terms: -4.38178046 + 4 = -0.38178046 x = -0.38178046 Simplifying x = -0.38178046Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.38178046, -0.38178046}
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