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Simplifying 2(x + -1) + -1(x + 3)(x + -3) = 0 Reorder the terms: 2(-1 + x) + -1(x + 3)(x + -3) = 0 (-1 * 2 + x * 2) + -1(x + 3)(x + -3) = 0 (-2 + 2x) + -1(x + 3)(x + -3) = 0 Reorder the terms: -2 + 2x + -1(3 + x)(x + -3) = 0 Reorder the terms: -2 + 2x + -1(3 + x)(-3 + x) = 0 Multiply (3 + x) * (-3 + x) -2 + 2x + -1(3(-3 + x) + x(-3 + x)) = 0 -2 + 2x + -1((-3 * 3 + x * 3) + x(-3 + x)) = 0 -2 + 2x + -1((-9 + 3x) + x(-3 + x)) = 0 -2 + 2x + -1(-9 + 3x + (-3 * x + x * x)) = 0 -2 + 2x + -1(-9 + 3x + (-3x + x2)) = 0 Combine like terms: 3x + -3x = 0 -2 + 2x + -1(-9 + 0 + x2) = 0 -2 + 2x + -1(-9 + x2) = 0 -2 + 2x + (-9 * -1 + x2 * -1) = 0 -2 + 2x + (9 + -1x2) = 0 Reorder the terms: -2 + 9 + 2x + -1x2 = 0 Combine like terms: -2 + 9 = 7 7 + 2x + -1x2 = 0 Solving 7 + 2x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -2x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -2x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -2x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x + x2 = 0 + 7 -2x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2x + x2 = 7 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 7 + 1 Reorder the terms: 1 + -2x + x2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2x + x2 = 8 Factor a perfect square on the left side: (x + -1)(x + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -1) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -1 = 2.828427125 Simplifying x + -1 = 2.828427125 Reorder the terms: -1 + x = 2.828427125 Solving -1 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.828427125 + 1 x = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 x = 3.828427125 Simplifying x = 3.828427125Subproblem 2
x + -1 = -2.828427125 Simplifying x + -1 = -2.828427125 Reorder the terms: -1 + x = -2.828427125 Solving -1 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.828427125 + 1 x = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 x = -1.828427125 Simplifying x = -1.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.828427125, -1.828427125}
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