1.7x^2+x-1.5=0

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Solution for 1.7x^2+x-1.5=0 equation:


Simplifying
1.7x2 + x + -1.5 = 0

Reorder the terms:
-1.5 + x + 1.7x2 = 0

Solving
-1.5 + x + 1.7x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.7'.
-0.8823529412 + 0.5882352941x + x2 = 0

Move the constant term to the right:

Add '0.8823529412' to each side of the equation.
-0.8823529412 + 0.5882352941x + 0.8823529412 + x2 = 0 + 0.8823529412

Reorder the terms:
-0.8823529412 + 0.8823529412 + 0.5882352941x + x2 = 0 + 0.8823529412

Combine like terms: -0.8823529412 + 0.8823529412 = 0.0000000000
0.0000000000 + 0.5882352941x + x2 = 0 + 0.8823529412
0.5882352941x + x2 = 0 + 0.8823529412

Combine like terms: 0 + 0.8823529412 = 0.8823529412
0.5882352941x + x2 = 0.8823529412

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5882352941x + 0.25 + x2 = 0.8823529412 + 0.25

Reorder the terms:
0.25 + 0.5882352941x + x2 = 0.8823529412 + 0.25

Combine like terms: 0.8823529412 + 0.25 = 1.1323529412
0.25 + 0.5882352941x + x2 = 1.1323529412

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.1323529412

Calculate the square root of the right side: 1.064120736

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.064120736 and -1.064120736.

Subproblem 1

x + 0.5 = 1.064120736 Simplifying x + 0.5 = 1.064120736 Reorder the terms: 0.5 + x = 1.064120736 Solving 0.5 + x = 1.064120736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.064120736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.064120736 + -0.5 x = 1.064120736 + -0.5 Combine like terms: 1.064120736 + -0.5 = 0.564120736 x = 0.564120736 Simplifying x = 0.564120736

Subproblem 2

x + 0.5 = -1.064120736 Simplifying x + 0.5 = -1.064120736 Reorder the terms: 0.5 + x = -1.064120736 Solving 0.5 + x = -1.064120736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.064120736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.064120736 + -0.5 x = -1.064120736 + -0.5 Combine like terms: -1.064120736 + -0.5 = -1.564120736 x = -1.564120736 Simplifying x = -1.564120736

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.564120736, -1.564120736}

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