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Simplifying 5(x + -5)(x + 1) + 6(x + -5) = 2 Reorder the terms: 5(-5 + x)(x + 1) + 6(x + -5) = 2 Reorder the terms: 5(-5 + x)(1 + x) + 6(x + -5) = 2 Multiply (-5 + x) * (1 + x) 5(-5(1 + x) + x(1 + x)) + 6(x + -5) = 2 5((1 * -5 + x * -5) + x(1 + x)) + 6(x + -5) = 2 5((-5 + -5x) + x(1 + x)) + 6(x + -5) = 2 5(-5 + -5x + (1 * x + x * x)) + 6(x + -5) = 2 5(-5 + -5x + (1x + x2)) + 6(x + -5) = 2 Combine like terms: -5x + 1x = -4x 5(-5 + -4x + x2) + 6(x + -5) = 2 (-5 * 5 + -4x * 5 + x2 * 5) + 6(x + -5) = 2 (-25 + -20x + 5x2) + 6(x + -5) = 2 Reorder the terms: -25 + -20x + 5x2 + 6(-5 + x) = 2 -25 + -20x + 5x2 + (-5 * 6 + x * 6) = 2 -25 + -20x + 5x2 + (-30 + 6x) = 2 Reorder the terms: -25 + -30 + -20x + 6x + 5x2 = 2 Combine like terms: -25 + -30 = -55 -55 + -20x + 6x + 5x2 = 2 Combine like terms: -20x + 6x = -14x -55 + -14x + 5x2 = 2 Solving -55 + -14x + 5x2 = 2 Solving for variable 'x'. Reorder the terms: -55 + -2 + -14x + 5x2 = 2 + -2 Combine like terms: -55 + -2 = -57 -57 + -14x + 5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -57 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.4 + -2.8x + x2 = 0 Move the constant term to the right: Add '11.4' to each side of the equation. -11.4 + -2.8x + 11.4 + x2 = 0 + 11.4 Reorder the terms: -11.4 + 11.4 + -2.8x + x2 = 0 + 11.4 Combine like terms: -11.4 + 11.4 = 0.0 0.0 + -2.8x + x2 = 0 + 11.4 -2.8x + x2 = 0 + 11.4 Combine like terms: 0 + 11.4 = 11.4 -2.8x + x2 = 11.4 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 11.4 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 11.4 + 1.96 Combine like terms: 11.4 + 1.96 = 13.36 1.96 + -2.8x + x2 = 13.36 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 13.36 Calculate the square root of the right side: 3.655133377 Break this problem into two subproblems by setting (x + -1.4) equal to 3.655133377 and -3.655133377.Subproblem 1
x + -1.4 = 3.655133377 Simplifying x + -1.4 = 3.655133377 Reorder the terms: -1.4 + x = 3.655133377 Solving -1.4 + x = 3.655133377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 3.655133377 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 3.655133377 + 1.4 x = 3.655133377 + 1.4 Combine like terms: 3.655133377 + 1.4 = 5.055133377 x = 5.055133377 Simplifying x = 5.055133377Subproblem 2
x + -1.4 = -3.655133377 Simplifying x + -1.4 = -3.655133377 Reorder the terms: -1.4 + x = -3.655133377 Solving -1.4 + x = -3.655133377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -3.655133377 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -3.655133377 + 1.4 x = -3.655133377 + 1.4 Combine like terms: -3.655133377 + 1.4 = -2.255133377 x = -2.255133377 Simplifying x = -2.255133377Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.055133377, -2.255133377}
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