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Simplifying (2x + -5)(x + 3) = 62 Reorder the terms: (-5 + 2x)(x + 3) = 62 Reorder the terms: (-5 + 2x)(3 + x) = 62 Multiply (-5 + 2x) * (3 + x) (-5(3 + x) + 2x * (3 + x)) = 62 ((3 * -5 + x * -5) + 2x * (3 + x)) = 62 ((-15 + -5x) + 2x * (3 + x)) = 62 (-15 + -5x + (3 * 2x + x * 2x)) = 62 (-15 + -5x + (6x + 2x2)) = 62 Combine like terms: -5x + 6x = 1x (-15 + 1x + 2x2) = 62 Solving -15 + 1x + 2x2 = 62 Solving for variable 'x'. Reorder the terms: -15 + -62 + 1x + 2x2 = 62 + -62 Combine like terms: -15 + -62 = -77 -77 + 1x + 2x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -77 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -38.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '38.5' to each side of the equation. -38.5 + 0.5x + 38.5 + x2 = 0 + 38.5 Reorder the terms: -38.5 + 38.5 + 0.5x + x2 = 0 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + 0.5x + x2 = 0 + 38.5 0.5x + x2 = 0 + 38.5 Combine like terms: 0 + 38.5 = 38.5 0.5x + x2 = 38.5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 38.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 38.5 + 0.0625 Combine like terms: 38.5 + 0.0625 = 38.5625 0.0625 + 0.5x + x2 = 38.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 38.5625 Calculate the square root of the right side: 6.209871174 Break this problem into two subproblems by setting (x + 0.25) equal to 6.209871174 and -6.209871174.Subproblem 1
x + 0.25 = 6.209871174 Simplifying x + 0.25 = 6.209871174 Reorder the terms: 0.25 + x = 6.209871174 Solving 0.25 + x = 6.209871174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 6.209871174 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 6.209871174 + -0.25 x = 6.209871174 + -0.25 Combine like terms: 6.209871174 + -0.25 = 5.959871174 x = 5.959871174 Simplifying x = 5.959871174Subproblem 2
x + 0.25 = -6.209871174 Simplifying x + 0.25 = -6.209871174 Reorder the terms: 0.25 + x = -6.209871174 Solving 0.25 + x = -6.209871174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -6.209871174 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -6.209871174 + -0.25 x = -6.209871174 + -0.25 Combine like terms: -6.209871174 + -0.25 = -6.459871174 x = -6.459871174 Simplifying x = -6.459871174Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.959871174, -6.459871174}
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