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Simplifying 7x2 + -14x + 5 = 0 Reorder the terms: 5 + -14x + 7x2 = 0 Solving 5 + -14x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + -2x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -2x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -2x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.7142857143 -2x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -2x + x2 = -0.7142857143 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 = -0.7142857143 + 1 Reorder the terms: 1 + -2x + x2 = -0.7142857143 + 1 Combine like terms: -0.7142857143 + 1 = 0.2857142857 1 + -2x + x2 = 0.2857142857 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.2857142857 Calculate the square root of the right side: 0.534522484 Break this problem into two subproblems by setting (x + -1) equal to 0.534522484 and -0.534522484.Subproblem 1
x + -1 = 0.534522484 Simplifying x + -1 = 0.534522484 Reorder the terms: -1 + x = 0.534522484 Solving -1 + x = 0.534522484 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 = 0.534522484 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.534522484 + 1 x = 0.534522484 + 1 Combine like terms: 0.534522484 + 1 = 1.534522484 x = 1.534522484 Simplifying x = 1.534522484Subproblem 2
x + -1 = -0.534522484 Simplifying x + -1 = -0.534522484 Reorder the terms: -1 + x = -0.534522484 Solving -1 + x = -0.534522484 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 = -0.534522484 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.534522484 + 1 x = -0.534522484 + 1 Combine like terms: -0.534522484 + 1 = 0.465477516 x = 0.465477516 Simplifying x = 0.465477516Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.534522484, 0.465477516}
| 7457435734785477437575775737857873577375d+84832843478872485872875878783585288378573573357828537578785357838785787355873=74727472734787387778472747437378874478783378384378278438787874327843 | | -6x+5=2x-9 | | 1/2x-20=30 | | 5-a=5 | | 3(3)-6= | | (2+4)/9=2x | | Onehalfx-20=30 | | p=2-p | | (3y+6)/11=-9 | | 12x^2+42x-18=0 | | 0.8+0.2=10 | | 78-16y=190 | | 20-3/5d=29 | | 3(6)-11= | | 7/10x-1=34 | | x^2-2x+8=2 | | 3d(-1)+14= | | 8(s-4)+10=38 | | 15/4=-r/8 | | y-5=-4/7x | | X*x+27=2 | | 36x^5-12x^3+6x^2=0 | | 144+46= | | X*x+x=32 | | 6n+6=96 | | 4x/100= | | 4y/5+32=28 | | c+ab=5 | | (n-5)*10=50 | | .02-.05x-.3x=-.68 | | s^2+4s-40=0 | | n/29-18=382 |