240-52x-2x^2=114

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Solution for 240-52x-2x^2=114 equation:


Simplifying
240 + -52x + -2x2 = 114

Solving
240 + -52x + -2x2 = 114

Solving for variable 'x'.

Reorder the terms:
240 + -114 + -52x + -2x2 = 114 + -114

Combine like terms: 240 + -114 = 126
126 + -52x + -2x2 = 114 + -114

Combine like terms: 114 + -114 = 0
126 + -52x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(63 + -26x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(63 + -26x + -1x2)' equal to zero and attempt to solve: Simplifying 63 + -26x + -1x2 = 0 Solving 63 + -26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + 26x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 26x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 26x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 26x + x2 = 0 + 63 26x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 26x + x2 = 63 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 63 + 169 Reorder the terms: 169 + 26x + x2 = 63 + 169 Combine like terms: 63 + 169 = 232 169 + 26x + x2 = 232 Factor a perfect square on the left side: (x + 13)(x + 13) = 232 Calculate the square root of the right side: 15.231546212 Break this problem into two subproblems by setting (x + 13) equal to 15.231546212 and -15.231546212.

Subproblem 1

x + 13 = 15.231546212 Simplifying x + 13 = 15.231546212 Reorder the terms: 13 + x = 15.231546212 Solving 13 + x = 15.231546212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 15.231546212 + -13 Combine like terms: 13 + -13 = 0 0 + x = 15.231546212 + -13 x = 15.231546212 + -13 Combine like terms: 15.231546212 + -13 = 2.231546212 x = 2.231546212 Simplifying x = 2.231546212

Subproblem 2

x + 13 = -15.231546212 Simplifying x + 13 = -15.231546212 Reorder the terms: 13 + x = -15.231546212 Solving 13 + x = -15.231546212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -15.231546212 + -13 Combine like terms: 13 + -13 = 0 0 + x = -15.231546212 + -13 x = -15.231546212 + -13 Combine like terms: -15.231546212 + -13 = -28.231546212 x = -28.231546212 Simplifying x = -28.231546212

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.231546212, -28.231546212}

Solution

x = {2.231546212, -28.231546212}

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