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Simplifying 3(x + -1)(x + -1) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) Reorder the terms: 3(-1 + x)(x + -1) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) Reorder the terms: 3(-1 + x)(-1 + x) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) Multiply (-1 + x) * (-1 + x) 3(-1(-1 + x) + x(-1 + x)) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) 3((-1 * -1 + x * -1) + x(-1 + x)) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) 3((1 + -1x) + x(-1 + x)) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) 3(1 + -1x + (-1 * x + x * x)) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) 3(1 + -1x + (-1x + x2)) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) Combine like terms: -1x + -1x = -2x 3(1 + -2x + x2) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) (1 * 3 + -2x * 3 + x2 * 3) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) (3 + -6x + 3x2) + -4(x + 2)(x + 2) + 1 = 2x(2x + 11) Reorder the terms: 3 + -6x + 3x2 + -4(2 + x)(x + 2) + 1 = 2x(2x + 11) Reorder the terms: 3 + -6x + 3x2 + -4(2 + x)(2 + x) + 1 = 2x(2x + 11) Multiply (2 + x) * (2 + x) 3 + -6x + 3x2 + -4(2(2 + x) + x(2 + x)) + 1 = 2x(2x + 11) 3 + -6x + 3x2 + -4((2 * 2 + x * 2) + x(2 + x)) + 1 = 2x(2x + 11) 3 + -6x + 3x2 + -4((4 + 2x) + x(2 + x)) + 1 = 2x(2x + 11) 3 + -6x + 3x2 + -4(4 + 2x + (2 * x + x * x)) + 1 = 2x(2x + 11) 3 + -6x + 3x2 + -4(4 + 2x + (2x + x2)) + 1 = 2x(2x + 11) Combine like terms: 2x + 2x = 4x 3 + -6x + 3x2 + -4(4 + 4x + x2) + 1 = 2x(2x + 11) 3 + -6x + 3x2 + (4 * -4 + 4x * -4 + x2 * -4) + 1 = 2x(2x + 11) 3 + -6x + 3x2 + (-16 + -16x + -4x2) + 1 = 2x(2x + 11) Reorder the terms: 3 + -16 + 1 + -6x + -16x + 3x2 + -4x2 = 2x(2x + 11) Combine like terms: 3 + -16 = -13 -13 + 1 + -6x + -16x + 3x2 + -4x2 = 2x(2x + 11) Combine like terms: -13 + 1 = -12 -12 + -6x + -16x + 3x2 + -4x2 = 2x(2x + 11) Combine like terms: -6x + -16x = -22x -12 + -22x + 3x2 + -4x2 = 2x(2x + 11) Combine like terms: 3x2 + -4x2 = -1x2 -12 + -22x + -1x2 = 2x(2x + 11) Reorder the terms: -12 + -22x + -1x2 = 2x(11 + 2x) -12 + -22x + -1x2 = (11 * 2x + 2x * 2x) -12 + -22x + -1x2 = (22x + 4x2) Solving -12 + -22x + -1x2 = 22x + 4x2 Solving for variable 'x'. Reorder the terms: -12 + -22x + -22x + -1x2 + -4x2 = 22x + 4x2 + -22x + -4x2 Combine like terms: -22x + -22x = -44x -12 + -44x + -1x2 + -4x2 = 22x + 4x2 + -22x + -4x2 Combine like terms: -1x2 + -4x2 = -5x2 -12 + -44x + -5x2 = 22x + 4x2 + -22x + -4x2 Reorder the terms: -12 + -44x + -5x2 = 22x + -22x + 4x2 + -4x2 Combine like terms: 22x + -22x = 0 -12 + -44x + -5x2 = 0 + 4x2 + -4x2 -12 + -44x + -5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -12 + -44x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 44x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 44x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + 44x + 5x2 = 0 Solving 12 + 44x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 8.8x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 8.8x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 8.8x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 8.8x + x2 = 0 + -2.4 8.8x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 8.8x + x2 = -2.4 The x term is 8.8x. Take half its coefficient (4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. 8.8x + 19.36 + x2 = -2.4 + 19.36 Reorder the terms: 19.36 + 8.8x + x2 = -2.4 + 19.36 Combine like terms: -2.4 + 19.36 = 16.96 19.36 + 8.8x + x2 = 16.96 Factor a perfect square on the left side: (x + 4.4)(x + 4.4) = 16.96 Calculate the square root of the right side: 4.118252056 Break this problem into two subproblems by setting (x + 4.4) equal to 4.118252056 and -4.118252056.Subproblem 1
x + 4.4 = 4.118252056 Simplifying x + 4.4 = 4.118252056 Reorder the terms: 4.4 + x = 4.118252056 Solving 4.4 + x = 4.118252056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = 4.118252056 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = 4.118252056 + -4.4 x = 4.118252056 + -4.4 Combine like terms: 4.118252056 + -4.4 = -0.281747944 x = -0.281747944 Simplifying x = -0.281747944Subproblem 2
x + 4.4 = -4.118252056 Simplifying x + 4.4 = -4.118252056 Reorder the terms: 4.4 + x = -4.118252056 Solving 4.4 + x = -4.118252056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = -4.118252056 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = -4.118252056 + -4.4 x = -4.118252056 + -4.4 Combine like terms: -4.118252056 + -4.4 = -8.518252056 x = -8.518252056 Simplifying x = -8.518252056Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.281747944, -8.518252056}Solution
x = {-0.281747944, -8.518252056}
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