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Simplifying -2x2 + 13x = -30 Reorder the terms: 13x + -2x2 = -30 Solving 13x + -2x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + 13x + -2x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -15 + -6.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -6.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -6.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -6.5x + x2 = 0 + 15 -6.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -6.5x + x2 = 15 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 = 15 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 15 + 10.5625 Combine like terms: 15 + 10.5625 = 25.5625 10.5625 + -6.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -3.25) equal to 5.055937104 and -5.055937104.Subproblem 1
x + -3.25 = 5.055937104 Simplifying x + -3.25 = 5.055937104 Reorder the terms: -3.25 + x = 5.055937104 Solving -3.25 + x = 5.055937104 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 = 5.055937104 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 5.055937104 + 3.25 x = 5.055937104 + 3.25 Combine like terms: 5.055937104 + 3.25 = 8.305937104 x = 8.305937104 Simplifying x = 8.305937104Subproblem 2
x + -3.25 = -5.055937104 Simplifying x + -3.25 = -5.055937104 Reorder the terms: -3.25 + x = -5.055937104 Solving -3.25 + x = -5.055937104 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 = -5.055937104 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -5.055937104 + 3.25 x = -5.055937104 + 3.25 Combine like terms: -5.055937104 + 3.25 = -1.805937104 x = -1.805937104 Simplifying x = -1.805937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.305937104, -1.805937104}
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