700=-15x^2+330x-815

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Solution for 700=-15x^2+330x-815 equation:


Simplifying
700 = -15x2 + 330x + -815

Reorder the terms:
700 = -815 + 330x + -15x2

Solving
700 = -815 + 330x + -15x2

Solving for variable 'x'.

Combine like terms: 700 + 815 = 1515
1515 + -330x + 15x2 = -815 + 330x + -15x2 + 815 + -330x + 15x2

Reorder the terms:
1515 + -330x + 15x2 = -815 + 815 + 330x + -330x + -15x2 + 15x2

Combine like terms: -815 + 815 = 0
1515 + -330x + 15x2 = 0 + 330x + -330x + -15x2 + 15x2
1515 + -330x + 15x2 = 330x + -330x + -15x2 + 15x2

Combine like terms: 330x + -330x = 0
1515 + -330x + 15x2 = 0 + -15x2 + 15x2
1515 + -330x + 15x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
1515 + -330x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(101 + -22x + x2) = 0

Ignore the factor 15.

Subproblem 1

Set the factor '(101 + -22x + x2)' equal to zero and attempt to solve: Simplifying 101 + -22x + x2 = 0 Solving 101 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-101' to each side of the equation. 101 + -22x + -101 + x2 = 0 + -101 Reorder the terms: 101 + -101 + -22x + x2 = 0 + -101 Combine like terms: 101 + -101 = 0 0 + -22x + x2 = 0 + -101 -22x + x2 = 0 + -101 Combine like terms: 0 + -101 = -101 -22x + x2 = -101 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -101 + 121 Reorder the terms: 121 + -22x + x2 = -101 + 121 Combine like terms: -101 + 121 = 20 121 + -22x + x2 = 20 Factor a perfect square on the left side: (x + -11)(x + -11) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -11) equal to 4.472135955 and -4.472135955.

Subproblem 1

x + -11 = 4.472135955 Simplifying x + -11 = 4.472135955 Reorder the terms: -11 + x = 4.472135955 Solving -11 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 4.472135955 + 11 Combine like terms: -11 + 11 = 0 0 + x = 4.472135955 + 11 x = 4.472135955 + 11 Combine like terms: 4.472135955 + 11 = 15.472135955 x = 15.472135955 Simplifying x = 15.472135955

Subproblem 2

x + -11 = -4.472135955 Simplifying x + -11 = -4.472135955 Reorder the terms: -11 + x = -4.472135955 Solving -11 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -4.472135955 + 11 Combine like terms: -11 + 11 = 0 0 + x = -4.472135955 + 11 x = -4.472135955 + 11 Combine like terms: -4.472135955 + 11 = 6.527864045 x = 6.527864045 Simplifying x = 6.527864045

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.472135955, 6.527864045}

Solution

x = {15.472135955, 6.527864045}

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