0=.1x^2+.14x-1.51

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Solution for 0=.1x^2+.14x-1.51 equation:


Simplifying
0 = 0.1x2 + 0.14x + -1.51

Reorder the terms:
0 = -1.51 + 0.14x + 0.1x2

Solving
0 = -1.51 + 0.14x + 0.1x2

Solving for variable 'x'.

Combine like terms: 0 + 1.51 = 1.51
1.51 + -0.14x + -0.1x2 = -1.51 + 0.14x + 0.1x2 + 1.51 + -0.14x + -0.1x2

Reorder the terms:
1.51 + -0.14x + -0.1x2 = -1.51 + 1.51 + 0.14x + -0.14x + 0.1x2 + -0.1x2

Combine like terms: -1.51 + 1.51 = 0.00
1.51 + -0.14x + -0.1x2 = 0.00 + 0.14x + -0.14x + 0.1x2 + -0.1x2
1.51 + -0.14x + -0.1x2 = 0.14x + -0.14x + 0.1x2 + -0.1x2

Combine like terms: 0.14x + -0.14x = 0.00
1.51 + -0.14x + -0.1x2 = 0.00 + 0.1x2 + -0.1x2
1.51 + -0.14x + -0.1x2 = 0.1x2 + -0.1x2

Combine like terms: 0.1x2 + -0.1x2 = 0.0
1.51 + -0.14x + -0.1x2 = 0.0

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
-15.1 + 1.4x + x2 = 0

Move the constant term to the right:

Add '15.1' to each side of the equation.
-15.1 + 1.4x + 15.1 + x2 = 0 + 15.1

Reorder the terms:
-15.1 + 15.1 + 1.4x + x2 = 0 + 15.1

Combine like terms: -15.1 + 15.1 = 0.0
0.0 + 1.4x + x2 = 0 + 15.1
1.4x + x2 = 0 + 15.1

Combine like terms: 0 + 15.1 = 15.1
1.4x + x2 = 15.1

The x term is 1.4x.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x + 0.49 + x2 = 15.1 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 15.1 + 0.49

Combine like terms: 15.1 + 0.49 = 15.59
0.49 + 1.4x + x2 = 15.59

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 15.59

Calculate the square root of the right side: 3.948417404

Break this problem into two subproblems by setting 
(x + 0.7) equal to 3.948417404 and -3.948417404.

Subproblem 1

x + 0.7 = 3.948417404 Simplifying x + 0.7 = 3.948417404 Reorder the terms: 0.7 + x = 3.948417404 Solving 0.7 + x = 3.948417404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 3.948417404 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 3.948417404 + -0.7 x = 3.948417404 + -0.7 Combine like terms: 3.948417404 + -0.7 = 3.248417404 x = 3.248417404 Simplifying x = 3.248417404

Subproblem 2

x + 0.7 = -3.948417404 Simplifying x + 0.7 = -3.948417404 Reorder the terms: 0.7 + x = -3.948417404 Solving 0.7 + x = -3.948417404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -3.948417404 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -3.948417404 + -0.7 x = -3.948417404 + -0.7 Combine like terms: -3.948417404 + -0.7 = -4.648417404 x = -4.648417404 Simplifying x = -4.648417404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.248417404, -4.648417404}

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