x^2-1.5x-90=0

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Solution for x^2-1.5x-90=0 equation:


Simplifying
x2 + -1.5x + -90 = 0

Reorder the terms:
-90 + -1.5x + x2 = 0

Solving
-90 + -1.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -1.5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -1.5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -1.5x + x2 = 0 + 90
-1.5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-1.5x + x2 = 90

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 90 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 90 + 0.5625

Combine like terms: 90 + 0.5625 = 90.5625
0.5625 + -1.5x + x2 = 90.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 90.5625

Calculate the square root of the right side: 9.516433155

Break this problem into two subproblems by setting 
(x + -0.75) equal to 9.516433155 and -9.516433155.

Subproblem 1

x + -0.75 = 9.516433155 Simplifying x + -0.75 = 9.516433155 Reorder the terms: -0.75 + x = 9.516433155 Solving -0.75 + x = 9.516433155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 9.516433155 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 9.516433155 + 0.75 x = 9.516433155 + 0.75 Combine like terms: 9.516433155 + 0.75 = 10.266433155 x = 10.266433155 Simplifying x = 10.266433155

Subproblem 2

x + -0.75 = -9.516433155 Simplifying x + -0.75 = -9.516433155 Reorder the terms: -0.75 + x = -9.516433155 Solving -0.75 + x = -9.516433155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -9.516433155 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -9.516433155 + 0.75 x = -9.516433155 + 0.75 Combine like terms: -9.516433155 + 0.75 = -8.766433155 x = -8.766433155 Simplifying x = -8.766433155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.266433155, -8.766433155}

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