-16x^2+23x+7=10

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Solution for -16x^2+23x+7=10 equation:


Simplifying
-16x2 + 23x + 7 = 10

Reorder the terms:
7 + 23x + -16x2 = 10

Solving
7 + 23x + -16x2 = 10

Solving for variable 'x'.

Reorder the terms:
7 + -10 + 23x + -16x2 = 10 + -10

Combine like terms: 7 + -10 = -3
-3 + 23x + -16x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-3 + 23x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.1875 + -1.4375x + x2 = 0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + -1.4375x + -0.1875 + x2 = 0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + -1.4375x + x2 = 0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + -1.4375x + x2 = 0 + -0.1875
-1.4375x + x2 = 0 + -0.1875

Combine like terms: 0 + -0.1875 = -0.1875
-1.4375x + x2 = -0.1875

The x term is -1.4375x.  Take half its coefficient (-0.71875).
Square it (0.5166015625) and add it to both sides.

Add '0.5166015625' to each side of the equation.
-1.4375x + 0.5166015625 + x2 = -0.1875 + 0.5166015625

Reorder the terms:
0.5166015625 + -1.4375x + x2 = -0.1875 + 0.5166015625

Combine like terms: -0.1875 + 0.5166015625 = 0.3291015625
0.5166015625 + -1.4375x + x2 = 0.3291015625

Factor a perfect square on the left side:
(x + -0.71875)(x + -0.71875) = 0.3291015625

Calculate the square root of the right side: 0.573673742

Break this problem into two subproblems by setting 
(x + -0.71875) equal to 0.573673742 and -0.573673742.

Subproblem 1

x + -0.71875 = 0.573673742 Simplifying x + -0.71875 = 0.573673742 Reorder the terms: -0.71875 + x = 0.573673742 Solving -0.71875 + x = 0.573673742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.71875' to each side of the equation. -0.71875 + 0.71875 + x = 0.573673742 + 0.71875 Combine like terms: -0.71875 + 0.71875 = 0.00000 0.00000 + x = 0.573673742 + 0.71875 x = 0.573673742 + 0.71875 Combine like terms: 0.573673742 + 0.71875 = 1.292423742 x = 1.292423742 Simplifying x = 1.292423742

Subproblem 2

x + -0.71875 = -0.573673742 Simplifying x + -0.71875 = -0.573673742 Reorder the terms: -0.71875 + x = -0.573673742 Solving -0.71875 + x = -0.573673742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.71875' to each side of the equation. -0.71875 + 0.71875 + x = -0.573673742 + 0.71875 Combine like terms: -0.71875 + 0.71875 = 0.00000 0.00000 + x = -0.573673742 + 0.71875 x = -0.573673742 + 0.71875 Combine like terms: -0.573673742 + 0.71875 = 0.145076258 x = 0.145076258 Simplifying x = 0.145076258

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.292423742, 0.145076258}

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