5x^2-150x+125=0

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Solution for 5x^2-150x+125=0 equation:


Simplifying
5x2 + -150x + 125 = 0

Reorder the terms:
125 + -150x + 5x2 = 0

Solving
125 + -150x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(25 + -30x + x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(25 + -30x + x2)' equal to zero and attempt to solve: Simplifying 25 + -30x + x2 = 0 Solving 25 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -30x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -30x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -30x + x2 = 0 + -25 -30x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -30x + x2 = -25 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -25 + 225 Reorder the terms: 225 + -30x + x2 = -25 + 225 Combine like terms: -25 + 225 = 200 225 + -30x + x2 = 200 Factor a perfect square on the left side: (x + -15)(x + -15) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -15) equal to 14.142135624 and -14.142135624.

Subproblem 1

x + -15 = 14.142135624 Simplifying x + -15 = 14.142135624 Reorder the terms: -15 + x = 14.142135624 Solving -15 + x = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 14.142135624 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.142135624 + 15 x = 14.142135624 + 15 Combine like terms: 14.142135624 + 15 = 29.142135624 x = 29.142135624 Simplifying x = 29.142135624

Subproblem 2

x + -15 = -14.142135624 Simplifying x + -15 = -14.142135624 Reorder the terms: -15 + x = -14.142135624 Solving -15 + x = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -14.142135624 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.142135624 + 15 x = -14.142135624 + 15 Combine like terms: -14.142135624 + 15 = 0.857864376 x = 0.857864376 Simplifying x = 0.857864376

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.142135624, 0.857864376}

Solution

x = {29.142135624, 0.857864376}

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