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Simplifying (-4x2 + -8x + 2) + -1(x2 + -4x + -1) = 0 Reorder the terms: (2 + -8x + -4x2) + -1(x2 + -4x + -1) = 0 Remove parenthesis around (2 + -8x + -4x2) 2 + -8x + -4x2 + -1(x2 + -4x + -1) = 0 Reorder the terms: 2 + -8x + -4x2 + -1(-1 + -4x + x2) = 0 2 + -8x + -4x2 + (-1 * -1 + -4x * -1 + x2 * -1) = 0 2 + -8x + -4x2 + (1 + 4x + -1x2) = 0 Reorder the terms: 2 + 1 + -8x + 4x + -4x2 + -1x2 = 0 Combine like terms: 2 + 1 = 3 3 + -8x + 4x + -4x2 + -1x2 = 0 Combine like terms: -8x + 4x = -4x 3 + -4x + -4x2 + -1x2 = 0 Combine like terms: -4x2 + -1x2 = -5x2 3 + -4x + -5x2 = 0 Solving 3 + -4x + -5x2 = 0 Solving for variable 'x'. 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 = 0.471779789 x = 0.471779789 Simplifying x = 0.471779789Subproblem 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 = -1.271779789 x = -1.271779789 Simplifying x = -1.271779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.471779789, -1.271779789}
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