3=-16x^2+90x+7

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Solution for 3=-16x^2+90x+7 equation:


Simplifying
3 = -16x2 + 90x + 7

Reorder the terms:
3 = 7 + 90x + -16x2

Solving
3 = 7 + 90x + -16x2

Solving for variable 'x'.

Combine like terms: 3 + -7 = -4
-4 + -90x + 16x2 = 7 + 90x + -16x2 + -7 + -90x + 16x2

Reorder the terms:
-4 + -90x + 16x2 = 7 + -7 + 90x + -90x + -16x2 + 16x2

Combine like terms: 7 + -7 = 0
-4 + -90x + 16x2 = 0 + 90x + -90x + -16x2 + 16x2
-4 + -90x + 16x2 = 90x + -90x + -16x2 + 16x2

Combine like terms: 90x + -90x = 0
-4 + -90x + 16x2 = 0 + -16x2 + 16x2
-4 + -90x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-4 + -90x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -45x + 8x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -45x + 8x2)' equal to zero and attempt to solve: Simplifying -2 + -45x + 8x2 = 0 Solving -2 + -45x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -5.625x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -5.625x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -5.625x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -5.625x + x2 = 0 + 0.25 -5.625x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -5.625x + x2 = 0.25 The x term is -5.625x. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625x + 7.91015625 + x2 = 0.25 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = 0.25 + 7.91015625 Combine like terms: 0.25 + 7.91015625 = 8.16015625 7.91015625 + -5.625x + x2 = 8.16015625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 8.16015625 Calculate the square root of the right side: 2.856598721 Break this problem into two subproblems by setting (x + -2.8125) equal to 2.856598721 and -2.856598721.

Subproblem 1

x + -2.8125 = 2.856598721 Simplifying x + -2.8125 = 2.856598721 Reorder the terms: -2.8125 + x = 2.856598721 Solving -2.8125 + x = 2.856598721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = 2.856598721 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 2.856598721 + 2.8125 x = 2.856598721 + 2.8125 Combine like terms: 2.856598721 + 2.8125 = 5.669098721 x = 5.669098721 Simplifying x = 5.669098721

Subproblem 2

x + -2.8125 = -2.856598721 Simplifying x + -2.8125 = -2.856598721 Reorder the terms: -2.8125 + x = -2.856598721 Solving -2.8125 + x = -2.856598721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = -2.856598721 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -2.856598721 + 2.8125 x = -2.856598721 + 2.8125 Combine like terms: -2.856598721 + 2.8125 = -0.044098721 x = -0.044098721 Simplifying x = -0.044098721

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.669098721, -0.044098721}

Solution

x = {5.669098721, -0.044098721}

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