24x^2+100x-26=0

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Solution for 24x^2+100x-26=0 equation:


Simplifying
24x2 + 100x + -26 = 0

Reorder the terms:
-26 + 100x + 24x2 = 0

Solving
-26 + 100x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 50x + 12x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-13 + 50x + 12x2)' equal to zero and attempt to solve: Simplifying -13 + 50x + 12x2 = 0 Solving -13 + 50x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.083333333 + 4.166666667x + x2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + 4.166666667x + 1.083333333 + x2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + 4.166666667x + x2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + 4.166666667x + x2 = 0 + 1.083333333 4.166666667x + x2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 4.166666667x + x2 = 1.083333333 The x term is 4.166666667x. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667x + 4.340277781 + x2 = 1.083333333 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667x + x2 = 1.083333333 + 4.340277781 Combine like terms: 1.083333333 + 4.340277781 = 5.423611114 4.340277781 + 4.166666667x + x2 = 5.423611114 Factor a perfect square on the left side: (x + 2.083333334)(x + 2.083333334) = 5.423611114 Calculate the square root of the right side: 2.328864769 Break this problem into two subproblems by setting (x + 2.083333334) equal to 2.328864769 and -2.328864769.

Subproblem 1

x + 2.083333334 = 2.328864769 Simplifying x + 2.083333334 = 2.328864769 Reorder the terms: 2.083333334 + x = 2.328864769 Solving 2.083333334 + x = 2.328864769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = 2.328864769 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = 2.328864769 + -2.083333334 x = 2.328864769 + -2.083333334 Combine like terms: 2.328864769 + -2.083333334 = 0.245531435 x = 0.245531435 Simplifying x = 0.245531435

Subproblem 2

x + 2.083333334 = -2.328864769 Simplifying x + 2.083333334 = -2.328864769 Reorder the terms: 2.083333334 + x = -2.328864769 Solving 2.083333334 + x = -2.328864769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + x = -2.328864769 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + x = -2.328864769 + -2.083333334 x = -2.328864769 + -2.083333334 Combine like terms: -2.328864769 + -2.083333334 = -4.412198103 x = -4.412198103 Simplifying x = -4.412198103

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.245531435, -4.412198103}

Solution

x = {0.245531435, -4.412198103}

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