5(5x^2-6x-14)=0

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Solution for 5(5x^2-6x-14)=0 equation:


Simplifying
5(5x2 + -6x + -14) = 0

Reorder the terms:
5(-14 + -6x + 5x2) = 0
(-14 * 5 + -6x * 5 + 5x2 * 5) = 0
(-70 + -30x + 25x2) = 0

Solving
-70 + -30x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-14 + -6x + 5x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-14 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying -14 + -6x + 5x2 = 0 Solving -14 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -1.2x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -1.2x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -1.2x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -1.2x + x2 = 0 + 2.8 -1.2x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -1.2x + x2 = 2.8 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 2.8 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 2.8 + 0.36 Combine like terms: 2.8 + 0.36 = 3.16 0.36 + -1.2x + x2 = 3.16 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (x + -0.6) equal to 1.777638883 and -1.777638883.

Subproblem 1

x + -0.6 = 1.777638883 Simplifying x + -0.6 = 1.777638883 Reorder the terms: -0.6 + x = 1.777638883 Solving -0.6 + x = 1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.777638883 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.777638883 + 0.6 x = 1.777638883 + 0.6 Combine like terms: 1.777638883 + 0.6 = 2.377638883 x = 2.377638883 Simplifying x = 2.377638883

Subproblem 2

x + -0.6 = -1.777638883 Simplifying x + -0.6 = -1.777638883 Reorder the terms: -0.6 + x = -1.777638883 Solving -0.6 + x = -1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.777638883 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.777638883 + 0.6 x = -1.777638883 + 0.6 Combine like terms: -1.777638883 + 0.6 = -1.177638883 x = -1.177638883 Simplifying x = -1.177638883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.377638883, -1.177638883}

Solution

x = {2.377638883, -1.177638883}

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