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Simplifying -0.25x2 + x + 3 = -1x + 7 Reorder the terms: 3 + x + -0.25x2 = -1x + 7 Reorder the terms: 3 + x + -0.25x2 = 7 + -1x Solving 3 + x + -0.25x2 = 7 + -1x Solving for variable 'x'. Reorder the terms: 3 + -7 + x + x + -0.25x2 = 7 + -1x + -7 + x Combine like terms: 3 + -7 = -4 -4 + x + x + -0.25x2 = 7 + -1x + -7 + x Combine like terms: x + x = 2x -4 + 2x + -0.25x2 = 7 + -1x + -7 + x Reorder the terms: -4 + 2x + -0.25x2 = 7 + -7 + -1x + x Combine like terms: 7 + -7 = 0 -4 + 2x + -0.25x2 = 0 + -1x + x -4 + 2x + -0.25x2 = -1x + x Combine like terms: -1x + x = 0 -4 + 2x + -0.25x2 = 0 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 16 + -8x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -8x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -8x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -8x + x2 = 0 + -16 -8x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -8x + x2 = -16 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 = -16 + 16 Reorder the terms: 16 + -8x + x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -8x + x2 = 0 Factor a perfect square on the left side: (x + -4)(x + -4) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -4) equal to 0 and 0.Subproblem 1
x + -4 = 0 Simplifying x + -4 = 0 Reorder the terms: -4 + x = 0 Solving -4 + x = 0 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 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -4 = 0 Simplifying x + -4 = 0 Reorder the terms: -4 + x = 0 Solving -4 + x = 0 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 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, 4}
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