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Simplifying 3x2 + 13x + -28 = 2x2 Reorder the terms: -28 + 13x + 3x2 = 2x2 Solving -28 + 13x + 3x2 = 2x2 Solving for variable 'x'. Combine like terms: 3x2 + -2x2 = 1x2 -28 + 13x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -28 + 13x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 13x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 13x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 13x + x2 = 0 + 28 13x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 13x + x2 = 28 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 = 28 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 28 + 42.25 Combine like terms: 28 + 42.25 = 70.25 42.25 + 13x + x2 = 70.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x + 6.5) equal to 8.381527307 and -8.381527307.Subproblem 1
x + 6.5 = 8.381527307 Simplifying x + 6.5 = 8.381527307 Reorder the terms: 6.5 + x = 8.381527307 Solving 6.5 + x = 8.381527307 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 = 8.381527307 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.381527307 + -6.5 x = 8.381527307 + -6.5 Combine like terms: 8.381527307 + -6.5 = 1.881527307 x = 1.881527307 Simplifying x = 1.881527307Subproblem 2
x + 6.5 = -8.381527307 Simplifying x + 6.5 = -8.381527307 Reorder the terms: 6.5 + x = -8.381527307 Solving 6.5 + x = -8.381527307 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 = -8.381527307 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.381527307 + -6.5 x = -8.381527307 + -6.5 Combine like terms: -8.381527307 + -6.5 = -14.881527307 x = -14.881527307 Simplifying x = -14.881527307Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.881527307, -14.881527307}
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