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Simplifying 2x2 + 8x + 3 = 4x2 + 5x + -1 Reorder the terms: 3 + 8x + 2x2 = 4x2 + 5x + -1 Reorder the terms: 3 + 8x + 2x2 = -1 + 5x + 4x2 Solving 3 + 8x + 2x2 = -1 + 5x + 4x2 Solving for variable 'x'. Reorder the terms: 3 + 1 + 8x + -5x + 2x2 + -4x2 = -1 + 5x + 4x2 + 1 + -5x + -4x2 Combine like terms: 3 + 1 = 4 4 + 8x + -5x + 2x2 + -4x2 = -1 + 5x + 4x2 + 1 + -5x + -4x2 Combine like terms: 8x + -5x = 3x 4 + 3x + 2x2 + -4x2 = -1 + 5x + 4x2 + 1 + -5x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 4 + 3x + -2x2 = -1 + 5x + 4x2 + 1 + -5x + -4x2 Reorder the terms: 4 + 3x + -2x2 = -1 + 1 + 5x + -5x + 4x2 + -4x2 Combine like terms: -1 + 1 = 0 4 + 3x + -2x2 = 0 + 5x + -5x + 4x2 + -4x2 4 + 3x + -2x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 4 + 3x + -2x2 = 0 + 4x2 + -4x2 4 + 3x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 4 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2 + -1.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.5x + x2 = 0 + 2 -1.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.5x + x2 = 2 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 2 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + -1.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -0.75) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -0.75 = 1.600781059 Simplifying x + -0.75 = 1.600781059 Reorder the terms: -0.75 + x = 1.600781059 Solving -0.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.600781059 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.600781059 + 0.75 x = 1.600781059 + 0.75 Combine like terms: 1.600781059 + 0.75 = 2.350781059 x = 2.350781059 Simplifying x = 2.350781059Subproblem 2
x + -0.75 = -1.600781059 Simplifying x + -0.75 = -1.600781059 Reorder the terms: -0.75 + x = -1.600781059 Solving -0.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.600781059 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.600781059 + 0.75 x = -1.600781059 + 0.75 Combine like terms: -1.600781059 + 0.75 = -0.850781059 x = -0.850781059 Simplifying x = -0.850781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.350781059, -0.850781059}
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