4.9x^2+10x-70=0

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Solution for 4.9x^2+10x-70=0 equation:


Simplifying
4.9x2 + 10x + -70 = 0

Reorder the terms:
-70 + 10x + 4.9x2 = 0

Solving
-70 + 10x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
-14.28571429 + 2.040816327x + x2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + 2.040816327x + 14.28571429 + x2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + 2.040816327x + x2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + 2.040816327x + x2 = 0 + 14.28571429
2.040816327x + x2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
2.040816327x + x2 = 14.28571429

The x term is 2.040816327x.  Take half its coefficient (1.020408164).
Square it (1.041232821) and add it to both sides.

Add '1.041232821' to each side of the equation.
2.040816327x + 1.041232821 + x2 = 14.28571429 + 1.041232821

Reorder the terms:
1.041232821 + 2.040816327x + x2 = 14.28571429 + 1.041232821

Combine like terms: 14.28571429 + 1.041232821 = 15.326947111
1.041232821 + 2.040816327x + x2 = 15.326947111

Factor a perfect square on the left side:
(x + 1.020408164)(x + 1.020408164) = 15.326947111

Calculate the square root of the right side: 3.91496451

Break this problem into two subproblems by setting 
(x + 1.020408164) equal to 3.91496451 and -3.91496451.

Subproblem 1

x + 1.020408164 = 3.91496451 Simplifying x + 1.020408164 = 3.91496451 Reorder the terms: 1.020408164 + x = 3.91496451 Solving 1.020408164 + x = 3.91496451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + x = 3.91496451 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = 3.91496451 + -1.020408164 x = 3.91496451 + -1.020408164 Combine like terms: 3.91496451 + -1.020408164 = 2.894556346 x = 2.894556346 Simplifying x = 2.894556346

Subproblem 2

x + 1.020408164 = -3.91496451 Simplifying x + 1.020408164 = -3.91496451 Reorder the terms: 1.020408164 + x = -3.91496451 Solving 1.020408164 + x = -3.91496451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + x = -3.91496451 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = -3.91496451 + -1.020408164 x = -3.91496451 + -1.020408164 Combine like terms: -3.91496451 + -1.020408164 = -4.935372674 x = -4.935372674 Simplifying x = -4.935372674

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.894556346, -4.935372674}

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