4x^2-12x+9=7

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Solution for 4x^2-12x+9=7 equation:


Simplifying
4x2 + -12x + 9 = 7

Reorder the terms:
9 + -12x + 4x2 = 7

Solving
9 + -12x + 4x2 = 7

Solving for variable 'x'.

Reorder the terms:
9 + -7 + -12x + 4x2 = 7 + -7

Combine like terms: 9 + -7 = 2
2 + -12x + 4x2 = 7 + -7

Combine like terms: 7 + -7 = 0
2 + -12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + -6x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + -6x + 2x2 = 0 Solving 1 + -6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -3x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3x + x2 = 0 + -0.5 -3x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3x + x2 = -0.5 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 = -0.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.5 + 2.25 Combine like terms: -0.5 + 2.25 = 1.75 2.25 + -3x + x2 = 1.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -1.5 = 1.322875656 Simplifying x + -1.5 = 1.322875656 Reorder the terms: -1.5 + x = 1.322875656 Solving -1.5 + x = 1.322875656 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 = 1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.322875656 + 1.5 x = 1.322875656 + 1.5 Combine like terms: 1.322875656 + 1.5 = 2.822875656 x = 2.822875656 Simplifying x = 2.822875656

Subproblem 2

x + -1.5 = -1.322875656 Simplifying x + -1.5 = -1.322875656 Reorder the terms: -1.5 + x = -1.322875656 Solving -1.5 + x = -1.322875656 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 = -1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.322875656 + 1.5 x = -1.322875656 + 1.5 Combine like terms: -1.322875656 + 1.5 = 0.177124344 x = 0.177124344 Simplifying x = 0.177124344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.822875656, 0.177124344}

Solution

x = {2.822875656, 0.177124344}

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