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Simplifying 0.5x + 3 = x2 + -4 Reorder the terms: 3 + 0.5x = x2 + -4 Reorder the terms: 3 + 0.5x = -4 + x2 Solving 3 + 0.5x = -4 + x2 Solving for variable 'x'. Reorder the terms: 3 + 4 + 0.5x + -1x2 = -4 + x2 + 4 + -1x2 Combine like terms: 3 + 4 = 7 7 + 0.5x + -1x2 = -4 + x2 + 4 + -1x2 Reorder the terms: 7 + 0.5x + -1x2 = -4 + 4 + x2 + -1x2 Combine like terms: -4 + 4 = 0 7 + 0.5x + -1x2 = 0 + x2 + -1x2 7 + 0.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + 0.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -0.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.5x + x2 = 0 + 7 -0.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.5x + x2 = 7 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 7 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 7 + 0.0625 Combine like terms: 7 + 0.0625 = 7.0625 0.0625 + -0.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -0.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -0.25 = 2.657536453 Simplifying x + -0.25 = 2.657536453 Reorder the terms: -0.25 + x = 2.657536453 Solving -0.25 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.657536453 + 0.25 x = 2.657536453 + 0.25 Combine like terms: 2.657536453 + 0.25 = 2.907536453 x = 2.907536453 Simplifying x = 2.907536453Subproblem 2
x + -0.25 = -2.657536453 Simplifying x + -0.25 = -2.657536453 Reorder the terms: -0.25 + x = -2.657536453 Solving -0.25 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.657536453 + 0.25 x = -2.657536453 + 0.25 Combine like terms: -2.657536453 + 0.25 = -2.407536453 x = -2.407536453 Simplifying x = -2.407536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.907536453, -2.407536453}
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