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Simplifying (x2 + x) + 4x(x + 1) + -12 = 0 Reorder the terms: (x + x2) + 4x(x + 1) + -12 = 0 Remove parenthesis around (x + x2) x + x2 + 4x(x + 1) + -12 = 0 Reorder the terms: x + x2 + 4x(1 + x) + -12 = 0 x + x2 + (1 * 4x + x * 4x) + -12 = 0 x + x2 + (4x + 4x2) + -12 = 0 Reorder the terms: -12 + x + 4x + x2 + 4x2 = 0 Combine like terms: x + 4x = 5x -12 + 5x + x2 + 4x2 = 0 Combine like terms: x2 + 4x2 = 5x2 -12 + 5x + 5x2 = 0 Solving -12 + 5x + 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'. -2.4 + x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x + x2 = 0 + 2.4 x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 x + x2 = 2.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 2.4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.4 + 0.25 Combine like terms: 2.4 + 0.25 = 2.65 1.25 + x2 = 2.65 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.65 Calculate the square root of the right side: 1.62788206 Break this problem into two subproblems by setting (x + 0.5) equal to 1.62788206 and -1.62788206.Subproblem 1
x + 0.5 = 1.62788206 Simplifying x + 0.5 = 1.62788206 Reorder the terms: 0.5 + x = 1.62788206 Solving 0.5 + x = 1.62788206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.62788206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.62788206 + -0.5 x = 1.62788206 + -0.5 Combine like terms: 1.62788206 + -0.5 = 1.12788206 x = 1.12788206 Simplifying x = 1.12788206Subproblem 2
x + 0.5 = -1.62788206 Simplifying x + 0.5 = -1.62788206 Reorder the terms: 0.5 + x = -1.62788206 Solving 0.5 + x = -1.62788206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.62788206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.62788206 + -0.5 x = -1.62788206 + -0.5 Combine like terms: -1.62788206 + -0.5 = -2.12788206 x = -2.12788206 Simplifying x = -2.12788206Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.12788206, -2.12788206}
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