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Simplifying 2x2 + -13x + -42 = 0 Reorder the terms: -42 + -13x + 2x2 = 0 Solving -42 + -13x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + -6.5x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -6.5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -6.5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -6.5x + x2 = 0 + 21 -6.5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -6.5x + x2 = 21 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 = 21 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 21 + 10.5625 Combine like terms: 21 + 10.5625 = 31.5625 10.5625 + -6.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + -3.25) equal to 5.618051264 and -5.618051264.Subproblem 1
x + -3.25 = 5.618051264 Simplifying x + -3.25 = 5.618051264 Reorder the terms: -3.25 + x = 5.618051264 Solving -3.25 + x = 5.618051264 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 = 5.618051264 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 5.618051264 + 3.25 x = 5.618051264 + 3.25 Combine like terms: 5.618051264 + 3.25 = 8.868051264 x = 8.868051264 Simplifying x = 8.868051264Subproblem 2
x + -3.25 = -5.618051264 Simplifying x + -3.25 = -5.618051264 Reorder the terms: -3.25 + x = -5.618051264 Solving -3.25 + x = -5.618051264 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 = -5.618051264 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -5.618051264 + 3.25 x = -5.618051264 + 3.25 Combine like terms: -5.618051264 + 3.25 = -2.368051264 x = -2.368051264 Simplifying x = -2.368051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.868051264, -2.368051264}
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