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Simplifying -1(4x + 2)(-3x + -5) = 3 Reorder the terms: -1(2 + 4x)(-3x + -5) = 3 Reorder the terms: -1(2 + 4x)(-5 + -3x) = 3 Multiply (2 + 4x) * (-5 + -3x) -1(2(-5 + -3x) + 4x * (-5 + -3x)) = 3 -1((-5 * 2 + -3x * 2) + 4x * (-5 + -3x)) = 3 -1((-10 + -6x) + 4x * (-5 + -3x)) = 3 -1(-10 + -6x + (-5 * 4x + -3x * 4x)) = 3 -1(-10 + -6x + (-20x + -12x2)) = 3 Combine like terms: -6x + -20x = -26x -1(-10 + -26x + -12x2) = 3 (-10 * -1 + -26x * -1 + -12x2 * -1) = 3 (10 + 26x + 12x2) = 3 Solving 10 + 26x + 12x2 = 3 Solving for variable 'x'. Reorder the terms: 10 + -3 + 26x + 12x2 = 3 + -3 Combine like terms: 10 + -3 = 7 7 + 26x + 12x2 = 3 + -3 Combine like terms: 3 + -3 = 0 7 + 26x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + 2.166666667x + -0.5833333333 + x2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + 2.166666667x + x2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + 2.166666667x + x2 = 0 + -0.5833333333 2.166666667x + x2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 2.166666667x + x2 = -0.5833333333 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = -0.5833333333 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = -0.5833333333 + 1.173611113 Combine like terms: -0.5833333333 + 1.173611113 = 0.5902777797 1.173611113 + 2.166666667x + x2 = 0.5902777797 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 0.5902777797 Calculate the square root of the right side: 0.768295373 Break this problem into two subproblems by setting (x + 1.083333334) equal to 0.768295373 and -0.768295373.Subproblem 1
x + 1.083333334 = 0.768295373 Simplifying x + 1.083333334 = 0.768295373 Reorder the terms: 1.083333334 + x = 0.768295373 Solving 1.083333334 + x = 0.768295373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 0.768295373 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 0.768295373 + -1.083333334 x = 0.768295373 + -1.083333334 Combine like terms: 0.768295373 + -1.083333334 = -0.315037961 x = -0.315037961 Simplifying x = -0.315037961Subproblem 2
x + 1.083333334 = -0.768295373 Simplifying x + 1.083333334 = -0.768295373 Reorder the terms: 1.083333334 + x = -0.768295373 Solving 1.083333334 + x = -0.768295373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -0.768295373 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -0.768295373 + -1.083333334 x = -0.768295373 + -1.083333334 Combine like terms: -0.768295373 + -1.083333334 = -1.851628707 x = -1.851628707 Simplifying x = -1.851628707Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.315037961, -1.851628707}
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