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Simplifying 90 + -26x = 2x2 Solving 90 + -26x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 0 90 + -26x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -13x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -13x + -1x2)' equal to zero and attempt to solve: Simplifying 45 + -13x + -1x2 = 0 Solving 45 + -13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + 13x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 13x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 13x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 13x + x2 = 0 + 45 13x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 13x + x2 = 45 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 45 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 45 + 42.25 Combine like terms: 45 + 42.25 = 87.25 42.25 + 13x + x2 = 87.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 87.25 Calculate the square root of the right side: 9.340770846 Break this problem into two subproblems by setting (x + 6.5) equal to 9.340770846 and -9.340770846.Subproblem 1
x + 6.5 = 9.340770846 Simplifying x + 6.5 = 9.340770846 Reorder the terms: 6.5 + x = 9.340770846 Solving 6.5 + x = 9.340770846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 9.340770846 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.340770846 + -6.5 x = 9.340770846 + -6.5 Combine like terms: 9.340770846 + -6.5 = 2.840770846 x = 2.840770846 Simplifying x = 2.840770846Subproblem 2
x + 6.5 = -9.340770846 Simplifying x + 6.5 = -9.340770846 Reorder the terms: 6.5 + x = -9.340770846 Solving 6.5 + x = -9.340770846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -9.340770846 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.340770846 + -6.5 x = -9.340770846 + -6.5 Combine like terms: -9.340770846 + -6.5 = -15.840770846 x = -15.840770846 Simplifying x = -15.840770846Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.840770846, -15.840770846}Solution
x = {2.840770846, -15.840770846}
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