15x^2-45x=15

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Solution for 15x^2-45x=15 equation:


Simplifying
15x2 + -45x = 15

Reorder the terms:
-45x + 15x2 = 15

Solving
-45x + 15x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -45x + 15x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -45x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-1 + -3x + x2) = 0

Ignore the factor 15.

Subproblem 1

Set the factor '(-1 + -3x + x2)' equal to zero and attempt to solve: Simplifying -1 + -3x + x2 = 0 Solving -1 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -3x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x + x2 = 0 + 1 -3x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3x + x2 = 1 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 1 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + -3x + x2 = 3.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

x + -1.5 = 1.802775638 Simplifying x + -1.5 = 1.802775638 Reorder the terms: -1.5 + x = 1.802775638 Solving -1.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.802775638 + 1.5 x = 1.802775638 + 1.5 Combine like terms: 1.802775638 + 1.5 = 3.302775638 x = 3.302775638 Simplifying x = 3.302775638

Subproblem 2

x + -1.5 = -1.802775638 Simplifying x + -1.5 = -1.802775638 Reorder the terms: -1.5 + x = -1.802775638 Solving -1.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.802775638 + 1.5 x = -1.802775638 + 1.5 Combine like terms: -1.802775638 + 1.5 = -0.302775638 x = -0.302775638 Simplifying x = -0.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.302775638, -0.302775638}

Solution

x = {3.302775638, -0.302775638}

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