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Simplifying (5x + 2)(x + -3) = 8 Reorder the terms: (2 + 5x)(x + -3) = 8 Reorder the terms: (2 + 5x)(-3 + x) = 8 Multiply (2 + 5x) * (-3 + x) (2(-3 + x) + 5x * (-3 + x)) = 8 ((-3 * 2 + x * 2) + 5x * (-3 + x)) = 8 ((-6 + 2x) + 5x * (-3 + x)) = 8 (-6 + 2x + (-3 * 5x + x * 5x)) = 8 (-6 + 2x + (-15x + 5x2)) = 8 Combine like terms: 2x + -15x = -13x (-6 + -13x + 5x2) = 8 Solving -6 + -13x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -6 + -8 + -13x + 5x2 = 8 + -8 Combine like terms: -6 + -8 = -14 -14 + -13x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -14 + -13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -2.6x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -2.6x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -2.6x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -2.6x + x2 = 0 + 2.8 -2.6x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -2.6x + x2 = 2.8 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = 2.8 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 2.8 + 1.69 Combine like terms: 2.8 + 1.69 = 4.49 1.69 + -2.6x + x2 = 4.49 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 4.49 Calculate the square root of the right side: 2.11896201 Break this problem into two subproblems by setting (x + -1.3) equal to 2.11896201 and -2.11896201.Subproblem 1
x + -1.3 = 2.11896201 Simplifying x + -1.3 = 2.11896201 Reorder the terms: -1.3 + x = 2.11896201 Solving -1.3 + x = 2.11896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 2.11896201 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 2.11896201 + 1.3 x = 2.11896201 + 1.3 Combine like terms: 2.11896201 + 1.3 = 3.41896201 x = 3.41896201 Simplifying x = 3.41896201Subproblem 2
x + -1.3 = -2.11896201 Simplifying x + -1.3 = -2.11896201 Reorder the terms: -1.3 + x = -2.11896201 Solving -1.3 + x = -2.11896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -2.11896201 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -2.11896201 + 1.3 x = -2.11896201 + 1.3 Combine like terms: -2.11896201 + 1.3 = -0.81896201 x = -0.81896201 Simplifying x = -0.81896201Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.41896201, -0.81896201}
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