0=50x^2+100x-70

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Solution for 0=50x^2+100x-70 equation:


Simplifying
0 = 50x2 + 100x + -70

Reorder the terms:
0 = -70 + 100x + 50x2

Solving
0 = -70 + 100x + 50x2

Solving for variable 'x'.

Combine like terms: 0 + 70 = 70
70 + -100x + -50x2 = -70 + 100x + 50x2 + 70 + -100x + -50x2

Reorder the terms:
70 + -100x + -50x2 = -70 + 70 + 100x + -100x + 50x2 + -50x2

Combine like terms: -70 + 70 = 0
70 + -100x + -50x2 = 0 + 100x + -100x + 50x2 + -50x2
70 + -100x + -50x2 = 100x + -100x + 50x2 + -50x2

Combine like terms: 100x + -100x = 0
70 + -100x + -50x2 = 0 + 50x2 + -50x2
70 + -100x + -50x2 = 50x2 + -50x2

Combine like terms: 50x2 + -50x2 = 0
70 + -100x + -50x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(7 + -10x + -5x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(7 + -10x + -5x2)' equal to zero and attempt to solve: Simplifying 7 + -10x + -5x2 = 0 Solving 7 + -10x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + 2x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 2x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 2x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 2x + x2 = 0 + 1.4 2x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 2x + x2 = 1.4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.4 + 1 Reorder the terms: 1 + 2x + x2 = 1.4 + 1 Combine like terms: 1.4 + 1 = 2.4 1 + 2x + x2 = 2.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.4 Calculate the square root of the right side: 1.549193338 Break this problem into two subproblems by setting (x + 1) equal to 1.549193338 and -1.549193338.

Subproblem 1

x + 1 = 1.549193338 Simplifying x + 1 = 1.549193338 Reorder the terms: 1 + x = 1.549193338 Solving 1 + x = 1.549193338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.549193338 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.549193338 + -1 x = 1.549193338 + -1 Combine like terms: 1.549193338 + -1 = 0.549193338 x = 0.549193338 Simplifying x = 0.549193338

Subproblem 2

x + 1 = -1.549193338 Simplifying x + 1 = -1.549193338 Reorder the terms: 1 + x = -1.549193338 Solving 1 + x = -1.549193338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.549193338 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.549193338 + -1 x = -1.549193338 + -1 Combine like terms: -1.549193338 + -1 = -2.549193338 x = -2.549193338 Simplifying x = -2.549193338

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.549193338, -2.549193338}

Solution

x = {0.549193338, -2.549193338}

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