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Simplifying ((x + -3)(x + -3)) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x Reorder the terms: ((-3 + x)(x + -3)) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x Reorder the terms: ((-3 + x)(-3 + x)) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x Multiply (-3 + x) * (-3 + x) ((-3(-3 + x) + x(-3 + x))) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x (((-3 * -3 + x * -3) + x(-3 + x))) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x (((9 + -3x) + x(-3 + x))) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x ((9 + -3x + (-3 * x + x * x))) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x ((9 + -3x + (-3x + x2))) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x Combine like terms: -3x + -3x = -6x ((9 + -6x + x2)) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x (9 + -6x + x2) + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x Remove parenthesis around (9 + -6x + x2) 9 + -6x + x2 + ((x + 1)(x + 1)) + (3x + -5) = 2x * 2x Reorder the terms: 9 + -6x + x2 + ((1 + x)(x + 1)) + (3x + -5) = 2x * 2x Reorder the terms: 9 + -6x + x2 + ((1 + x)(1 + x)) + (3x + -5) = 2x * 2x Multiply (1 + x) * (1 + x) 9 + -6x + x2 + ((1(1 + x) + x(1 + x))) + (3x + -5) = 2x * 2x 9 + -6x + x2 + (((1 * 1 + x * 1) + x(1 + x))) + (3x + -5) = 2x * 2x 9 + -6x + x2 + (((1 + 1x) + x(1 + x))) + (3x + -5) = 2x * 2x 9 + -6x + x2 + ((1 + 1x + (1 * x + x * x))) + (3x + -5) = 2x * 2x 9 + -6x + x2 + ((1 + 1x + (1x + x2))) + (3x + -5) = 2x * 2x Combine like terms: 1x + 1x = 2x 9 + -6x + x2 + ((1 + 2x + x2)) + (3x + -5) = 2x * 2x 9 + -6x + x2 + (1 + 2x + x2) + (3x + -5) = 2x * 2x Remove parenthesis around (1 + 2x + x2) 9 + -6x + x2 + 1 + 2x + x2 + (3x + -5) = 2x * 2x Reorder the terms: 9 + -6x + x2 + 1 + 2x + x2 + (-5 + 3x) = 2x * 2x Remove parenthesis around (-5 + 3x) 9 + -6x + x2 + 1 + 2x + x2 + -5 + 3x = 2x * 2x Reorder the terms: 9 + 1 + -5 + -6x + 2x + 3x + x2 + x2 = 2x * 2x Combine like terms: 9 + 1 = 10 10 + -5 + -6x + 2x + 3x + x2 + x2 = 2x * 2x Combine like terms: 10 + -5 = 5 5 + -6x + 2x + 3x + x2 + x2 = 2x * 2x Combine like terms: -6x + 2x = -4x 5 + -4x + 3x + x2 + x2 = 2x * 2x Combine like terms: -4x + 3x = -1x 5 + -1x + x2 + x2 = 2x * 2x Combine like terms: x2 + x2 = 2x2 5 + -1x + 2x2 = 2x * 2x Reorder the terms for easier multiplication: 5 + -1x + 2x2 = 2 * 2x * x Multiply 2 * 2 5 + -1x + 2x2 = 4x * x Multiply x * x 5 + -1x + 2x2 = 4x2 Solving 5 + -1x + 2x2 = 4x2 Solving for variable 'x'. Combine like terms: 2x2 + -4x2 = -2x2 5 + -1x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 5 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.5x + x2 = 0 + 2.5 0.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.5x + x2 = 2.5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 2.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2.5 + 0.0625 Combine like terms: 2.5 + 0.0625 = 2.5625 0.0625 + 0.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + 0.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + 0.25 = 1.600781059 Simplifying x + 0.25 = 1.600781059 Reorder the terms: 0.25 + x = 1.600781059 Solving 0.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.600781059 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.600781059 + -0.25 x = 1.600781059 + -0.25 Combine like terms: 1.600781059 + -0.25 = 1.350781059 x = 1.350781059 Simplifying x = 1.350781059Subproblem 2
x + 0.25 = -1.600781059 Simplifying x + 0.25 = -1.600781059 Reorder the terms: 0.25 + x = -1.600781059 Solving 0.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.600781059 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.600781059 + -0.25 x = -1.600781059 + -0.25 Combine like terms: -1.600781059 + -0.25 = -1.850781059 x = -1.850781059 Simplifying x = -1.850781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.350781059, -1.850781059}
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