-4.9x^2+15x+18=0

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Solution for -4.9x^2+15x+18=0 equation:


Simplifying
-4.9x2 + 15x + 18 = 0

Reorder the terms:
18 + 15x + -4.9x2 = 0

Solving
18 + 15x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-3.673469388 + -3.06122449x + x2 = 0

Move the constant term to the right:

Add '3.673469388' to each side of the equation.
-3.673469388 + -3.06122449x + 3.673469388 + x2 = 0 + 3.673469388

Reorder the terms:
-3.673469388 + 3.673469388 + -3.06122449x + x2 = 0 + 3.673469388

Combine like terms: -3.673469388 + 3.673469388 = 0.000000000
0.000000000 + -3.06122449x + x2 = 0 + 3.673469388
-3.06122449x + x2 = 0 + 3.673469388

Combine like terms: 0 + 3.673469388 = 3.673469388
-3.06122449x + x2 = 3.673469388

The x term is -3.06122449x.  Take half its coefficient (-1.530612245).
Square it (2.342773845) and add it to both sides.

Add '2.342773845' to each side of the equation.
-3.06122449x + 2.342773845 + x2 = 3.673469388 + 2.342773845

Reorder the terms:
2.342773845 + -3.06122449x + x2 = 3.673469388 + 2.342773845

Combine like terms: 3.673469388 + 2.342773845 = 6.016243233
2.342773845 + -3.06122449x + x2 = 6.016243233

Factor a perfect square on the left side:
(x + -1.530612245)(x + -1.530612245) = 6.016243233

Calculate the square root of the right side: 2.452803138

Break this problem into two subproblems by setting 
(x + -1.530612245) equal to 2.452803138 and -2.452803138.

Subproblem 1

x + -1.530612245 = 2.452803138 Simplifying x + -1.530612245 = 2.452803138 Reorder the terms: -1.530612245 + x = 2.452803138 Solving -1.530612245 + x = 2.452803138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + x = 2.452803138 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 2.452803138 + 1.530612245 x = 2.452803138 + 1.530612245 Combine like terms: 2.452803138 + 1.530612245 = 3.983415383 x = 3.983415383 Simplifying x = 3.983415383

Subproblem 2

x + -1.530612245 = -2.452803138 Simplifying x + -1.530612245 = -2.452803138 Reorder the terms: -1.530612245 + x = -2.452803138 Solving -1.530612245 + x = -2.452803138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + x = -2.452803138 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -2.452803138 + 1.530612245 x = -2.452803138 + 1.530612245 Combine like terms: -2.452803138 + 1.530612245 = -0.922190893 x = -0.922190893 Simplifying x = -0.922190893

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.983415383, -0.922190893}

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