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Simplifying (2x2 + x + 4) + (-3 + 7x + 8x2) = 0 Reorder the terms: (4 + x + 2x2) + (-3 + 7x + 8x2) = 0 Remove parenthesis around (4 + x + 2x2) 4 + x + 2x2 + (-3 + 7x + 8x2) = 0 Remove parenthesis around (-3 + 7x + 8x2) 4 + x + 2x2 + -3 + 7x + 8x2 = 0 Reorder the terms: 4 + -3 + x + 7x + 2x2 + 8x2 = 0 Combine like terms: 4 + -3 = 1 1 + x + 7x + 2x2 + 8x2 = 0 Combine like terms: x + 7x = 8x 1 + 8x + 2x2 + 8x2 = 0 Combine like terms: 2x2 + 8x2 = 10x2 1 + 8x + 10x2 = 0 Solving 1 + 8x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + 0.8x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 0.8x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + 0.8x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 0.8x + x2 = 0.0 + -0.1 0.8x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 0.8x + x2 = -0.1 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 = -0.1 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = -0.1 + 0.16 Combine like terms: -0.1 + 0.16 = 0.06 0.16 + 0.8x + x2 = 0.06 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.06 Calculate the square root of the right side: 0.244948974 Break this problem into two subproblems by setting (x + 0.4) equal to 0.244948974 and -0.244948974.Subproblem 1
x + 0.4 = 0.244948974 Simplifying x + 0.4 = 0.244948974 Reorder the terms: 0.4 + x = 0.244948974 Solving 0.4 + x = 0.244948974 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 = 0.244948974 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.244948974 + -0.4 x = 0.244948974 + -0.4 Combine like terms: 0.244948974 + -0.4 = -0.155051026 x = -0.155051026 Simplifying x = -0.155051026Subproblem 2
x + 0.4 = -0.244948974 Simplifying x + 0.4 = -0.244948974 Reorder the terms: 0.4 + x = -0.244948974 Solving 0.4 + x = -0.244948974 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 = -0.244948974 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.244948974 + -0.4 x = -0.244948974 + -0.4 Combine like terms: -0.244948974 + -0.4 = -0.644948974 x = -0.644948974 Simplifying x = -0.644948974Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.155051026, -0.644948974}
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