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Simplifying 2x2 + 16x = 7 Reorder the terms: 16x + 2x2 = 7 Solving 16x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 16x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 8x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 8x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 8x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 8x + x2 = 0 + 3.5 8x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 8x + x2 = 3.5 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 = 3.5 + 16 Reorder the terms: 16 + 8x + x2 = 3.5 + 16 Combine like terms: 3.5 + 16 = 19.5 16 + 8x + x2 = 19.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (x + 4) equal to 4.415880433 and -4.415880433.Subproblem 1
x + 4 = 4.415880433 Simplifying x + 4 = 4.415880433 Reorder the terms: 4 + x = 4.415880433 Solving 4 + x = 4.415880433 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 = 4.415880433 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.415880433 + -4 x = 4.415880433 + -4 Combine like terms: 4.415880433 + -4 = 0.415880433 x = 0.415880433 Simplifying x = 0.415880433Subproblem 2
x + 4 = -4.415880433 Simplifying x + 4 = -4.415880433 Reorder the terms: 4 + x = -4.415880433 Solving 4 + x = -4.415880433 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 = -4.415880433 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.415880433 + -4 x = -4.415880433 + -4 Combine like terms: -4.415880433 + -4 = -8.415880433 x = -8.415880433 Simplifying x = -8.415880433Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.415880433, -8.415880433}
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