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Simplifying (x + -2) + -1(x + -1)(3 + -2x) = 3(x + 3)(x + -3) + 25 Reorder the terms: (-2 + x) + -1(x + -1)(3 + -2x) = 3(x + 3)(x + -3) + 25 Remove parenthesis around (-2 + x) -2 + x + -1(x + -1)(3 + -2x) = 3(x + 3)(x + -3) + 25 Reorder the terms: -2 + x + -1(-1 + x)(3 + -2x) = 3(x + 3)(x + -3) + 25 Multiply (-1 + x) * (3 + -2x) -2 + x + -1(-1(3 + -2x) + x(3 + -2x)) = 3(x + 3)(x + -3) + 25 -2 + x + -1((3 * -1 + -2x * -1) + x(3 + -2x)) = 3(x + 3)(x + -3) + 25 -2 + x + -1((-3 + 2x) + x(3 + -2x)) = 3(x + 3)(x + -3) + 25 -2 + x + -1(-3 + 2x + (3 * x + -2x * x)) = 3(x + 3)(x + -3) + 25 -2 + x + -1(-3 + 2x + (3x + -2x2)) = 3(x + 3)(x + -3) + 25 Combine like terms: 2x + 3x = 5x -2 + x + -1(-3 + 5x + -2x2) = 3(x + 3)(x + -3) + 25 -2 + x + (-3 * -1 + 5x * -1 + -2x2 * -1) = 3(x + 3)(x + -3) + 25 -2 + x + (3 + -5x + 2x2) = 3(x + 3)(x + -3) + 25 Reorder the terms: -2 + 3 + x + -5x + 2x2 = 3(x + 3)(x + -3) + 25 Combine like terms: -2 + 3 = 1 1 + x + -5x + 2x2 = 3(x + 3)(x + -3) + 25 Combine like terms: x + -5x = -4x 1 + -4x + 2x2 = 3(x + 3)(x + -3) + 25 Reorder the terms: 1 + -4x + 2x2 = 3(3 + x)(x + -3) + 25 Reorder the terms: 1 + -4x + 2x2 = 3(3 + x)(-3 + x) + 25 Multiply (3 + x) * (-3 + x) 1 + -4x + 2x2 = 3(3(-3 + x) + x(-3 + x)) + 25 1 + -4x + 2x2 = 3((-3 * 3 + x * 3) + x(-3 + x)) + 25 1 + -4x + 2x2 = 3((-9 + 3x) + x(-3 + x)) + 25 1 + -4x + 2x2 = 3(-9 + 3x + (-3 * x + x * x)) + 25 1 + -4x + 2x2 = 3(-9 + 3x + (-3x + x2)) + 25 Combine like terms: 3x + -3x = 0 1 + -4x + 2x2 = 3(-9 + 0 + x2) + 25 1 + -4x + 2x2 = 3(-9 + x2) + 25 1 + -4x + 2x2 = (-9 * 3 + x2 * 3) + 25 1 + -4x + 2x2 = (-27 + 3x2) + 25 Reorder the terms: 1 + -4x + 2x2 = -27 + 25 + 3x2 Combine like terms: -27 + 25 = -2 1 + -4x + 2x2 = -2 + 3x2 Solving 1 + -4x + 2x2 = -2 + 3x2 Solving for variable 'x'. Reorder the terms: 1 + 2 + -4x + 2x2 + -3x2 = -2 + 3x2 + 2 + -3x2 Combine like terms: 1 + 2 = 3 3 + -4x + 2x2 + -3x2 = -2 + 3x2 + 2 + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 3 + -4x + -1x2 = -2 + 3x2 + 2 + -3x2 Reorder the terms: 3 + -4x + -1x2 = -2 + 2 + 3x2 + -3x2 Combine like terms: -2 + 2 = 0 3 + -4x + -1x2 = 0 + 3x2 + -3x2 3 + -4x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 3 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x + x2 = 0 + 3 4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4x + x2 = 3 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3 + 4 Reorder the terms: 4 + 4x + x2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4x + x2 = 7 Factor a perfect square on the left side: (x + 2)(x + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 2 = 2.645751311 Simplifying x + 2 = 2.645751311 Reorder the terms: 2 + x = 2.645751311 Solving 2 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.645751311 + -2 x = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 x = 0.645751311 Simplifying x = 0.645751311Subproblem 2
x + 2 = -2.645751311 Simplifying x + 2 = -2.645751311 Reorder the terms: 2 + x = -2.645751311 Solving 2 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.645751311 + -2 x = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 x = -4.645751311 Simplifying x = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.645751311, -4.645751311}
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