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Simplifying 5(x + -1) + -1(5x + 4)(x + -3) = -2 Reorder the terms: 5(-1 + x) + -1(5x + 4)(x + -3) = -2 (-1 * 5 + x * 5) + -1(5x + 4)(x + -3) = -2 (-5 + 5x) + -1(5x + 4)(x + -3) = -2 Reorder the terms: -5 + 5x + -1(4 + 5x)(x + -3) = -2 Reorder the terms: -5 + 5x + -1(4 + 5x)(-3 + x) = -2 Multiply (4 + 5x) * (-3 + x) -5 + 5x + -1(4(-3 + x) + 5x * (-3 + x)) = -2 -5 + 5x + -1((-3 * 4 + x * 4) + 5x * (-3 + x)) = -2 -5 + 5x + -1((-12 + 4x) + 5x * (-3 + x)) = -2 -5 + 5x + -1(-12 + 4x + (-3 * 5x + x * 5x)) = -2 -5 + 5x + -1(-12 + 4x + (-15x + 5x2)) = -2 Combine like terms: 4x + -15x = -11x -5 + 5x + -1(-12 + -11x + 5x2) = -2 -5 + 5x + (-12 * -1 + -11x * -1 + 5x2 * -1) = -2 -5 + 5x + (12 + 11x + -5x2) = -2 Reorder the terms: -5 + 12 + 5x + 11x + -5x2 = -2 Combine like terms: -5 + 12 = 7 7 + 5x + 11x + -5x2 = -2 Combine like terms: 5x + 11x = 16x 7 + 16x + -5x2 = -2 Solving 7 + 16x + -5x2 = -2 Solving for variable 'x'. Reorder the terms: 7 + 2 + 16x + -5x2 = -2 + 2 Combine like terms: 7 + 2 = 9 9 + 16x + -5x2 = -2 + 2 Combine like terms: -2 + 2 = 0 9 + 16x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.8 + -3.2x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -3.2x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -3.2x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -3.2x + x2 = 0 + 1.8 -3.2x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -3.2x + x2 = 1.8 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 1.8 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 1.8 + 2.56 Combine like terms: 1.8 + 2.56 = 4.36 2.56 + -3.2x + x2 = 4.36 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (x + -1.6) equal to 2.088061302 and -2.088061302.Subproblem 1
x + -1.6 = 2.088061302 Simplifying x + -1.6 = 2.088061302 Reorder the terms: -1.6 + x = 2.088061302 Solving -1.6 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 2.088061302 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 2.088061302 + 1.6 x = 2.088061302 + 1.6 Combine like terms: 2.088061302 + 1.6 = 3.688061302 x = 3.688061302 Simplifying x = 3.688061302Subproblem 2
x + -1.6 = -2.088061302 Simplifying x + -1.6 = -2.088061302 Reorder the terms: -1.6 + x = -2.088061302 Solving -1.6 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -2.088061302 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -2.088061302 + 1.6 x = -2.088061302 + 1.6 Combine like terms: -2.088061302 + 1.6 = -0.488061302 x = -0.488061302 Simplifying x = -0.488061302Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.688061302, -0.488061302}
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