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Simplifying 2x2 + -49x = 7x2 + -5x + -32 Reorder the terms: -49x + 2x2 = 7x2 + -5x + -32 Reorder the terms: -49x + 2x2 = -32 + -5x + 7x2 Solving -49x + 2x2 = -32 + -5x + 7x2 Solving for variable 'x'. Reorder the terms: 32 + -49x + 5x + 2x2 + -7x2 = -32 + -5x + 7x2 + 32 + 5x + -7x2 Combine like terms: -49x + 5x = -44x 32 + -44x + 2x2 + -7x2 = -32 + -5x + 7x2 + 32 + 5x + -7x2 Combine like terms: 2x2 + -7x2 = -5x2 32 + -44x + -5x2 = -32 + -5x + 7x2 + 32 + 5x + -7x2 Reorder the terms: 32 + -44x + -5x2 = -32 + 32 + -5x + 5x + 7x2 + -7x2 Combine like terms: -32 + 32 = 0 32 + -44x + -5x2 = 0 + -5x + 5x + 7x2 + -7x2 32 + -44x + -5x2 = -5x + 5x + 7x2 + -7x2 Combine like terms: -5x + 5x = 0 32 + -44x + -5x2 = 0 + 7x2 + -7x2 32 + -44x + -5x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 32 + -44x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6.4 + 8.8x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 8.8x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 8.8x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 8.8x + x2 = 0 + 6.4 8.8x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 8.8x + x2 = 6.4 The x term is 8.8x. Take half its coefficient (4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. 8.8x + 19.36 + x2 = 6.4 + 19.36 Reorder the terms: 19.36 + 8.8x + x2 = 6.4 + 19.36 Combine like terms: 6.4 + 19.36 = 25.76 19.36 + 8.8x + x2 = 25.76 Factor a perfect square on the left side: (x + 4.4)(x + 4.4) = 25.76 Calculate the square root of the right side: 5.075431016 Break this problem into two subproblems by setting (x + 4.4) equal to 5.075431016 and -5.075431016.Subproblem 1
x + 4.4 = 5.075431016 Simplifying x + 4.4 = 5.075431016 Reorder the terms: 4.4 + x = 5.075431016 Solving 4.4 + x = 5.075431016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = 5.075431016 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = 5.075431016 + -4.4 x = 5.075431016 + -4.4 Combine like terms: 5.075431016 + -4.4 = 0.675431016 x = 0.675431016 Simplifying x = 0.675431016Subproblem 2
x + 4.4 = -5.075431016 Simplifying x + 4.4 = -5.075431016 Reorder the terms: 4.4 + x = -5.075431016 Solving 4.4 + x = -5.075431016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = -5.075431016 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = -5.075431016 + -4.4 x = -5.075431016 + -4.4 Combine like terms: -5.075431016 + -4.4 = -9.475431016 x = -9.475431016 Simplifying x = -9.475431016Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.675431016, -9.475431016}
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