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Simplifying -2x2 + 4x + 5 = 3x2 + 2 Reorder the terms: 5 + 4x + -2x2 = 3x2 + 2 Reorder the terms: 5 + 4x + -2x2 = 2 + 3x2 Solving 5 + 4x + -2x2 = 2 + 3x2 Solving for variable 'x'. Reorder the terms: 5 + -2 + 4x + -2x2 + -3x2 = 2 + 3x2 + -2 + -3x2 Combine like terms: 5 + -2 = 3 3 + 4x + -2x2 + -3x2 = 2 + 3x2 + -2 + -3x2 Combine like terms: -2x2 + -3x2 = -5x2 3 + 4x + -5x2 = 2 + 3x2 + -2 + -3x2 Reorder the terms: 3 + 4x + -5x2 = 2 + -2 + 3x2 + -3x2 Combine like terms: 2 + -2 = 0 3 + 4x + -5x2 = 0 + 3x2 + -3x2 3 + 4x + -5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 3 + 4x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.8x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.8x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.8x + x2 = 0 + 0.6 -0.8x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.8x + x2 = 0.6 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.6 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.6 + 0.16 Combine like terms: 0.6 + 0.16 = 0.76 0.16 + -0.8x + x2 = 0.76 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + -0.4) equal to 0.871779789 and -0.871779789.Subproblem 1
x + -0.4 = 0.871779789 Simplifying x + -0.4 = 0.871779789 Reorder the terms: -0.4 + x = 0.871779789 Solving -0.4 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.871779789 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.871779789 + 0.4 x = 0.871779789 + 0.4 Combine like terms: 0.871779789 + 0.4 = 1.271779789 x = 1.271779789 Simplifying x = 1.271779789Subproblem 2
x + -0.4 = -0.871779789 Simplifying x + -0.4 = -0.871779789 Reorder the terms: -0.4 + x = -0.871779789 Solving -0.4 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.871779789 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.871779789 + 0.4 x = -0.871779789 + 0.4 Combine like terms: -0.871779789 + 0.4 = -0.471779789 x = -0.471779789 Simplifying x = -0.471779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.271779789, -0.471779789}
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