10x*10x-60x-270=0

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Solution for 10x*10x-60x-270=0 equation:


Simplifying
10x * 10x + -60x + -270 = 0

Reorder the terms for easier multiplication:
10 * 10x * x + -60x + -270 = 0

Multiply 10 * 10
100x * x + -60x + -270 = 0

Multiply x * x
100x2 + -60x + -270 = 0

Reorder the terms:
-270 + -60x + 100x2 = 0

Solving
-270 + -60x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-27 + -6x + 10x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(-27 + -6x + 10x2)' equal to zero and attempt to solve: Simplifying -27 + -6x + 10x2 = 0 Solving -27 + -6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.7 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + -0.6x + 2.7 + x2 = 0.0 + 2.7 Reorder the terms: -2.7 + 2.7 + -0.6x + x2 = 0.0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + -0.6x + x2 = 0.0 + 2.7 -0.6x + x2 = 0.0 + 2.7 Combine like terms: 0.0 + 2.7 = 2.7 -0.6x + x2 = 2.7 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 2.7 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 2.7 + 0.09 Combine like terms: 2.7 + 0.09 = 2.79 0.09 + -0.6x + x2 = 2.79 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 2.79 Calculate the square root of the right side: 1.670329309 Break this problem into two subproblems by setting (x + -0.3) equal to 1.670329309 and -1.670329309.

Subproblem 1

x + -0.3 = 1.670329309 Simplifying x + -0.3 = 1.670329309 Reorder the terms: -0.3 + x = 1.670329309 Solving -0.3 + x = 1.670329309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.670329309 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.670329309 + 0.3 x = 1.670329309 + 0.3 Combine like terms: 1.670329309 + 0.3 = 1.970329309 x = 1.970329309 Simplifying x = 1.970329309

Subproblem 2

x + -0.3 = -1.670329309 Simplifying x + -0.3 = -1.670329309 Reorder the terms: -0.3 + x = -1.670329309 Solving -0.3 + x = -1.670329309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.670329309 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.670329309 + 0.3 x = -1.670329309 + 0.3 Combine like terms: -1.670329309 + 0.3 = -1.370329309 x = -1.370329309 Simplifying x = -1.370329309

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.970329309, -1.370329309}

Solution

x = {1.970329309, -1.370329309}

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