49x^2-84x=-29

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Solution for 49x^2-84x=-29 equation:


Simplifying
49x2 + -84x = -29

Reorder the terms:
-84x + 49x2 = -29

Solving
-84x + 49x2 = -29

Solving for variable 'x'.

Reorder the terms:
29 + -84x + 49x2 = -29 + 29

Combine like terms: -29 + 29 = 0
29 + -84x + 49x2 = 0

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

Divide each side by '49'.
0.5918367347 + -1.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.5918367347' to each side of the equation.
0.5918367347 + -1.714285714x + -0.5918367347 + x2 = 0 + -0.5918367347

Reorder the terms:
0.5918367347 + -0.5918367347 + -1.714285714x + x2 = 0 + -0.5918367347

Combine like terms: 0.5918367347 + -0.5918367347 = 0.0000000000
0.0000000000 + -1.714285714x + x2 = 0 + -0.5918367347
-1.714285714x + x2 = 0 + -0.5918367347

Combine like terms: 0 + -0.5918367347 = -0.5918367347
-1.714285714x + x2 = -0.5918367347

The x term is -1.714285714x.  Take half its coefficient (-0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
-1.714285714x + 0.7346938773 + x2 = -0.5918367347 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714x + x2 = -0.5918367347 + 0.7346938773

Combine like terms: -0.5918367347 + 0.7346938773 = 0.1428571426
0.7346938773 + -1.714285714x + x2 = 0.1428571426

Factor a perfect square on the left side:
(x + -0.857142857)(x + -0.857142857) = 0.1428571426

Calculate the square root of the right side: 0.377964473

Break this problem into two subproblems by setting 
(x + -0.857142857) equal to 0.377964473 and -0.377964473.

Subproblem 1

x + -0.857142857 = 0.377964473 Simplifying x + -0.857142857 = 0.377964473 Reorder the terms: -0.857142857 + x = 0.377964473 Solving -0.857142857 + x = 0.377964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 0.377964473 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 0.377964473 + 0.857142857 x = 0.377964473 + 0.857142857 Combine like terms: 0.377964473 + 0.857142857 = 1.23510733 x = 1.23510733 Simplifying x = 1.23510733

Subproblem 2

x + -0.857142857 = -0.377964473 Simplifying x + -0.857142857 = -0.377964473 Reorder the terms: -0.857142857 + x = -0.377964473 Solving -0.857142857 + x = -0.377964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -0.377964473 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -0.377964473 + 0.857142857 x = -0.377964473 + 0.857142857 Combine like terms: -0.377964473 + 0.857142857 = 0.479178384 x = 0.479178384 Simplifying x = 0.479178384

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.23510733, 0.479178384}

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