-5x(4x+7)+(-1+6x)=

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Solution for -5x(4x+7)+(-1+6x)= equation:


Simplifying
-5x(4x + 7) + (-1 + 6x) = 0

Reorder the terms:
-5x(7 + 4x) + (-1 + 6x) = 0
(7 * -5x + 4x * -5x) + (-1 + 6x) = 0
(-35x + -20x2) + (-1 + 6x) = 0

Remove parenthesis around (-1 + 6x)
-35x + -20x2 + -1 + 6x = 0

Reorder the terms:
-1 + -35x + 6x + -20x2 = 0

Combine like terms: -35x + 6x = -29x
-1 + -29x + -20x2 = 0

Solving
-1 + -29x + -20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 29x + 20x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(1 + 29x + 20x2)' equal to zero and attempt to solve: Simplifying 1 + 29x + 20x2 = 0 Solving 1 + 29x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.05 + 1.45x + x2 = 0.0 Move the constant term to the right: Add '-0.05' to each side of the equation. 0.05 + 1.45x + -0.05 + x2 = 0.0 + -0.05 Reorder the terms: 0.05 + -0.05 + 1.45x + x2 = 0.0 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + 1.45x + x2 = 0.0 + -0.05 1.45x + x2 = 0.0 + -0.05 Combine like terms: 0.0 + -0.05 = -0.05 1.45x + x2 = -0.05 The x term is 1.45x. Take half its coefficient (0.725). Square it (0.525625) and add it to both sides. Add '0.525625' to each side of the equation. 1.45x + 0.525625 + x2 = -0.05 + 0.525625 Reorder the terms: 0.525625 + 1.45x + x2 = -0.05 + 0.525625 Combine like terms: -0.05 + 0.525625 = 0.475625 0.525625 + 1.45x + x2 = 0.475625 Factor a perfect square on the left side: (x + 0.725)(x + 0.725) = 0.475625 Calculate the square root of the right side: 0.689655711 Break this problem into two subproblems by setting (x + 0.725) equal to 0.689655711 and -0.689655711.

Subproblem 1

x + 0.725 = 0.689655711 Simplifying x + 0.725 = 0.689655711 Reorder the terms: 0.725 + x = 0.689655711 Solving 0.725 + x = 0.689655711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.725' to each side of the equation. 0.725 + -0.725 + x = 0.689655711 + -0.725 Combine like terms: 0.725 + -0.725 = 0.000 0.000 + x = 0.689655711 + -0.725 x = 0.689655711 + -0.725 Combine like terms: 0.689655711 + -0.725 = -0.035344289 x = -0.035344289 Simplifying x = -0.035344289

Subproblem 2

x + 0.725 = -0.689655711 Simplifying x + 0.725 = -0.689655711 Reorder the terms: 0.725 + x = -0.689655711 Solving 0.725 + x = -0.689655711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.725' to each side of the equation. 0.725 + -0.725 + x = -0.689655711 + -0.725 Combine like terms: 0.725 + -0.725 = 0.000 0.000 + x = -0.689655711 + -0.725 x = -0.689655711 + -0.725 Combine like terms: -0.689655711 + -0.725 = -1.414655711 x = -1.414655711 Simplifying x = -1.414655711

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.035344289, -1.414655711}

Solution

x = {-0.035344289, -1.414655711}

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