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Simplifying 3x2 + -4 = x2 + x + 3 Reorder the terms: -4 + 3x2 = x2 + x + 3 Reorder the terms: -4 + 3x2 = 3 + x + x2 Solving -4 + 3x2 = 3 + x + x2 Solving for variable 'x'. Reorder the terms: -4 + -3 + -1x + 3x2 + -1x2 = 3 + x + x2 + -3 + -1x + -1x2 Combine like terms: -4 + -3 = -7 -7 + -1x + 3x2 + -1x2 = 3 + x + x2 + -3 + -1x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -7 + -1x + 2x2 = 3 + x + x2 + -3 + -1x + -1x2 Reorder the terms: -7 + -1x + 2x2 = 3 + -3 + x + -1x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -7 + -1x + 2x2 = 0 + x + -1x + x2 + -1x2 -7 + -1x + 2x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 -7 + -1x + 2x2 = 0 + x2 + -1x2 -7 + -1x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.5x + x2 = 0 + 3.5 -0.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.5x + x2 = 3.5 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 = 3.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 3.5 + 0.0625 Combine like terms: 3.5 + 0.0625 = 3.5625 0.0625 + -0.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + -0.25) equal to 1.887458609 and -1.887458609.Subproblem 1
x + -0.25 = 1.887458609 Simplifying x + -0.25 = 1.887458609 Reorder the terms: -0.25 + x = 1.887458609 Solving -0.25 + x = 1.887458609 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 = 1.887458609 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.887458609 + 0.25 x = 1.887458609 + 0.25 Combine like terms: 1.887458609 + 0.25 = 2.137458609 x = 2.137458609 Simplifying x = 2.137458609Subproblem 2
x + -0.25 = -1.887458609 Simplifying x + -0.25 = -1.887458609 Reorder the terms: -0.25 + x = -1.887458609 Solving -0.25 + x = -1.887458609 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 = -1.887458609 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.887458609 + 0.25 x = -1.887458609 + 0.25 Combine like terms: -1.887458609 + 0.25 = -1.637458609 x = -1.637458609 Simplifying x = -1.637458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.137458609, -1.637458609}
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