0=-7x^2+4x+9

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Solution for 0=-7x^2+4x+9 equation:


Simplifying
0 = -7x2 + 4x + 9

Reorder the terms:
0 = 9 + 4x + -7x2

Solving
0 = 9 + 4x + -7x2

Solving for variable 'x'.

Combine like terms: 0 + -9 = -9
-9 + -4x + 7x2 = 9 + 4x + -7x2 + -9 + -4x + 7x2

Reorder the terms:
-9 + -4x + 7x2 = 9 + -9 + 4x + -4x + -7x2 + 7x2

Combine like terms: 9 + -9 = 0
-9 + -4x + 7x2 = 0 + 4x + -4x + -7x2 + 7x2
-9 + -4x + 7x2 = 4x + -4x + -7x2 + 7x2

Combine like terms: 4x + -4x = 0
-9 + -4x + 7x2 = 0 + -7x2 + 7x2
-9 + -4x + 7x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-9 + -4x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-1.285714286 + -0.5714285714x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + -0.5714285714x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + -0.5714285714x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -0.5714285714x + x2 = 0 + 1.285714286
-0.5714285714x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
-0.5714285714x + x2 = 1.285714286

The x term is -0.5714285714x.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714x + 0.08163265305 + x2 = 1.285714286 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714x + x2 = 1.285714286 + 0.08163265305

Combine like terms: 1.285714286 + 0.08163265305 = 1.36734693905
0.08163265305 + -0.5714285714x + x2 = 1.36734693905

Factor a perfect square on the left side:
(x + -0.2857142857)(x + -0.2857142857) = 1.36734693905

Calculate the square root of the right side: 1.16933611

Break this problem into two subproblems by setting 
(x + -0.2857142857) equal to 1.16933611 and -1.16933611.

Subproblem 1

x + -0.2857142857 = 1.16933611 Simplifying x + -0.2857142857 = 1.16933611 Reorder the terms: -0.2857142857 + x = 1.16933611 Solving -0.2857142857 + x = 1.16933611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 1.16933611 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.16933611 + 0.2857142857 x = 1.16933611 + 0.2857142857 Combine like terms: 1.16933611 + 0.2857142857 = 1.4550503957 x = 1.4550503957 Simplifying x = 1.4550503957

Subproblem 2

x + -0.2857142857 = -1.16933611 Simplifying x + -0.2857142857 = -1.16933611 Reorder the terms: -0.2857142857 + x = -1.16933611 Solving -0.2857142857 + x = -1.16933611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -1.16933611 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.16933611 + 0.2857142857 x = -1.16933611 + 0.2857142857 Combine like terms: -1.16933611 + 0.2857142857 = -0.8836218243 x = -0.8836218243 Simplifying x = -0.8836218243

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4550503957, -0.8836218243}

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