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Simplifying (4x)(4x) + (x + 1)(x + 1) = (5x + -1)(5x + -1) Remove parenthesis around (4x) 4x(4x) + (x + 1)(x + 1) = (5x + -1)(5x + -1) Remove parenthesis around (4x) 4x * 4x + (x + 1)(x + 1) = (5x + -1)(5x + -1) Reorder the terms for easier multiplication: 4 * 4x * x + (x + 1)(x + 1) = (5x + -1)(5x + -1) Multiply 4 * 4 16x * x + (x + 1)(x + 1) = (5x + -1)(5x + -1) Multiply x * x 16x2 + (x + 1)(x + 1) = (5x + -1)(5x + -1) Reorder the terms: 16x2 + (1 + x)(x + 1) = (5x + -1)(5x + -1) Reorder the terms: 16x2 + (1 + x)(1 + x) = (5x + -1)(5x + -1) Multiply (1 + x) * (1 + x) 16x2 + (1(1 + x) + x(1 + x)) = (5x + -1)(5x + -1) 16x2 + ((1 * 1 + x * 1) + x(1 + x)) = (5x + -1)(5x + -1) 16x2 + ((1 + 1x) + x(1 + x)) = (5x + -1)(5x + -1) 16x2 + (1 + 1x + (1 * x + x * x)) = (5x + -1)(5x + -1) 16x2 + (1 + 1x + (1x + x2)) = (5x + -1)(5x + -1) Combine like terms: 1x + 1x = 2x 16x2 + (1 + 2x + x2) = (5x + -1)(5x + -1) Reorder the terms: 1 + 2x + 16x2 + x2 = (5x + -1)(5x + -1) Combine like terms: 16x2 + x2 = 17x2 1 + 2x + 17x2 = (5x + -1)(5x + -1) Reorder the terms: 1 + 2x + 17x2 = (-1 + 5x)(5x + -1) Reorder the terms: 1 + 2x + 17x2 = (-1 + 5x)(-1 + 5x) Multiply (-1 + 5x) * (-1 + 5x) 1 + 2x + 17x2 = (-1(-1 + 5x) + 5x * (-1 + 5x)) 1 + 2x + 17x2 = ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) 1 + 2x + 17x2 = ((1 + -5x) + 5x * (-1 + 5x)) 1 + 2x + 17x2 = (1 + -5x + (-1 * 5x + 5x * 5x)) 1 + 2x + 17x2 = (1 + -5x + (-5x + 25x2)) Combine like terms: -5x + -5x = -10x 1 + 2x + 17x2 = (1 + -10x + 25x2) Add '-1' to each side of the equation. 1 + 2x + -1 + 17x2 = 1 + -10x + -1 + 25x2 Reorder the terms: 1 + -1 + 2x + 17x2 = 1 + -10x + -1 + 25x2 Combine like terms: 1 + -1 = 0 0 + 2x + 17x2 = 1 + -10x + -1 + 25x2 2x + 17x2 = 1 + -10x + -1 + 25x2 Reorder the terms: 2x + 17x2 = 1 + -1 + -10x + 25x2 Combine like terms: 1 + -1 = 0 2x + 17x2 = 0 + -10x + 25x2 2x + 17x2 = -10x + 25x2 Solving 2x + 17x2 = -10x + 25x2 Solving for variable 'x'. Reorder the terms: 2x + 10x + 17x2 + -25x2 = -10x + 25x2 + 10x + -25x2 Combine like terms: 2x + 10x = 12x 12x + 17x2 + -25x2 = -10x + 25x2 + 10x + -25x2 Combine like terms: 17x2 + -25x2 = -8x2 12x + -8x2 = -10x + 25x2 + 10x + -25x2 Reorder the terms: 12x + -8x2 = -10x + 10x + 25x2 + -25x2 Combine like terms: -10x + 10x = 0 12x + -8x2 = 0 + 25x2 + -25x2 12x + -8x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 12x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(3 + -2x) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5}
| 5x+12=30-9x | | 5x^6-16x^4-x^3-5=0 | | cotx+2=0 | | 4x+(x+1)=5x-1 | | 5x-20=3-8 | | A/H=B/ | | x-(x-3)+(2x+1)=14 | | 5ln(x+1)=x | | T^3=0.125 | | 12x-5=8x+13 | | 5-(3x+2.5)=1 | | x^2+x=183 | | X^2+8x-y=0 | | 126/567= | | 7x-5=5x+10 | | 7/9*18/63= | | a*((64-2a)/2) | | 7/9*18/63 | | a^2-b^2=1000 | | a^2+b^2=1000 | | (X-3)2=14-2x | | 4x-12=54-4x | | ctg(x)=0 | | 0=ctg(0.5x)-1 | | 4cosx+5sinx=6 | | X^2y+y^3=0 | | 27x^2-27x=0 | | z^2-(3-i)z+4-3i=0 | | 3(x-15)=18 | | (D^3+D^2-8D-12)y=0 | | (10x+6)+(12-4x)=0 | | 3x-(5x+10)=6 |