10=(-16x^2)+32x+80

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Solution for 10=(-16x^2)+32x+80 equation:


Simplifying
10 = (-16x2) + 32x + 80

Reorder the terms:
10 = 80 + 32x + (-16x2)

Solving
10 = 80 + 32x + (-16x2)

Solving for variable 'x'.

Combine like terms: 10 + -80 = -70
-70 + -32x + (16x2) = 80 + 32x + (-16x2) + -80 + -32x + (16x2)

Reorder the terms:
-70 + -32x + (16x2) = 80 + -80 + 32x + -32x + (-16x2) + (16x2)

Combine like terms: 80 + -80 = 0
-70 + -32x + (16x2) = 0 + 32x + -32x + (-16x2) + (16x2)
-70 + -32x + (16x2) = 32x + -32x + (-16x2) + (16x2)

Combine like terms: 32x + -32x = 0
-70 + -32x + (16x2) = 0 + (-16x2) + (16x2)
-70 + -32x + (16x2) = (-16x2) + (16x2)

Combine like terms: (-16x2) + (16x2) = 0
-70 + -32x + (16x2) = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -16x + (8x2)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-35 + -16x + (8x2))' equal to zero and attempt to solve: Simplifying -35 + -16x + (8x2) = 0 Solving -35 + -16x + (8x2) = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + -2x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + -2x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + -2x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + -2x + x2 = 0 + 4.375 -2x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 -2x + x2 = 4.375 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 = 4.375 + 1 Reorder the terms: 1 + -2x + x2 = 4.375 + 1 Combine like terms: 4.375 + 1 = 5.375 1 + -2x + x2 = 5.375 Factor a perfect square on the left side: ((x) + -1)((x) + -1) = 5.375 Calculate the square root of the right side: 2.318404624 Break this problem into two subproblems by setting ((x) + -1) equal to 2.318404624 and -2.318404624.

Subproblem 1

(x) + -1 = 2.318404624 Simplifying (x) + -1 = 2.318404624 x + -1 = 2.318404624 Reorder the terms: -1 + x = 2.318404624 Solving -1 + x = 2.318404624 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 = 2.318404624 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.318404624 + 1 x = 2.318404624 + 1 Combine like terms: 2.318404624 + 1 = 3.318404624 x = 3.318404624 Simplifying x = 3.318404624

Subproblem 2

(x) + -1 = -2.318404624 Simplifying (x) + -1 = -2.318404624 x + -1 = -2.318404624 Reorder the terms: -1 + x = -2.318404624 Solving -1 + x = -2.318404624 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 = -2.318404624 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.318404624 + 1 x = -2.318404624 + 1 Combine like terms: -2.318404624 + 1 = -1.318404624 x = -1.318404624 Simplifying x = -1.318404624

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.318404624, -1.318404624}

Solution

x = {3.318404624, -1.318404624}

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