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Simplifying 2x2 + 9 = 13x Reorder the terms: 9 + 2x2 = 13x Solving 9 + 2x2 = 13x Solving for variable 'x'. Reorder the terms: 9 + -13x + 2x2 = 13x + -13x Combine like terms: 13x + -13x = 0 9 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -6.5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -6.5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -6.5x + x2 = 0 + -4.5 -6.5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -6.5x + x2 = -4.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -4.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -4.5 + 10.5625 Combine like terms: -4.5 + 10.5625 = 6.0625 10.5625 + -6.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -3.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -3.25 = 2.46221445 Simplifying x + -3.25 = 2.46221445 Reorder the terms: -3.25 + x = 2.46221445 Solving -3.25 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.46221445 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.46221445 + 3.25 x = 2.46221445 + 3.25 Combine like terms: 2.46221445 + 3.25 = 5.71221445 x = 5.71221445 Simplifying x = 5.71221445Subproblem 2
x + -3.25 = -2.46221445 Simplifying x + -3.25 = -2.46221445 Reorder the terms: -3.25 + x = -2.46221445 Solving -3.25 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.46221445 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.46221445 + 3.25 x = -2.46221445 + 3.25 Combine like terms: -2.46221445 + 3.25 = 0.78778555 x = 0.78778555 Simplifying x = 0.78778555Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.71221445, 0.78778555}
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