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Simplifying 0.5x2 + 2x = 3x + 7 Reorder the terms: 2x + 0.5x2 = 3x + 7 Reorder the terms: 2x + 0.5x2 = 7 + 3x Solving 2x + 0.5x2 = 7 + 3x Solving for variable 'x'. Reorder the terms: -7 + 2x + -3x + 0.5x2 = 7 + 3x + -7 + -3x Combine like terms: 2x + -3x = -1x -7 + -1x + 0.5x2 = 7 + 3x + -7 + -3x Reorder the terms: -7 + -1x + 0.5x2 = 7 + -7 + 3x + -3x Combine like terms: 7 + -7 = 0 -7 + -1x + 0.5x2 = 0 + 3x + -3x -7 + -1x + 0.5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -7 + -1x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -14 + -2x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -2x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -2x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2x + x2 = 0 + 14 -2x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -2x + x2 = 14 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 = 14 + 1 Reorder the terms: 1 + -2x + x2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + -2x + x2 = 15 Factor a perfect square on the left side: (x + -1)(x + -1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -1) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -1 = 3.872983346 Simplifying x + -1 = 3.872983346 Reorder the terms: -1 + x = 3.872983346 Solving -1 + x = 3.872983346 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 = 3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.872983346 + 1 x = 3.872983346 + 1 Combine like terms: 3.872983346 + 1 = 4.872983346 x = 4.872983346 Simplifying x = 4.872983346Subproblem 2
x + -1 = -3.872983346 Simplifying x + -1 = -3.872983346 Reorder the terms: -1 + x = -3.872983346 Solving -1 + x = -3.872983346 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 = -3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.872983346 + 1 x = -3.872983346 + 1 Combine like terms: -3.872983346 + 1 = -2.872983346 x = -2.872983346 Simplifying x = -2.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.872983346, -2.872983346}
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