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Simplifying 3x + -1x(4x + 5) = -1x(x + 4) + -3x + -5 Reorder the terms: 3x + -1x(5 + 4x) = -1x(x + 4) + -3x + -5 3x + (5 * -1x + 4x * -1x) = -1x(x + 4) + -3x + -5 3x + (-5x + -4x2) = -1x(x + 4) + -3x + -5 Combine like terms: 3x + -5x = -2x -2x + -4x2 = -1x(x + 4) + -3x + -5 Reorder the terms: -2x + -4x2 = -1x(4 + x) + -3x + -5 -2x + -4x2 = (4 * -1x + x * -1x) + -3x + -5 -2x + -4x2 = (-4x + -1x2) + -3x + -5 Reorder the terms: -2x + -4x2 = -5 + -4x + -3x + -1x2 Combine like terms: -4x + -3x = -7x -2x + -4x2 = -5 + -7x + -1x2 Solving -2x + -4x2 = -5 + -7x + -1x2 Solving for variable 'x'. Reorder the terms: 5 + -2x + 7x + -4x2 + x2 = -5 + -7x + -1x2 + 5 + 7x + x2 Combine like terms: -2x + 7x = 5x 5 + 5x + -4x2 + x2 = -5 + -7x + -1x2 + 5 + 7x + x2 Combine like terms: -4x2 + x2 = -3x2 5 + 5x + -3x2 = -5 + -7x + -1x2 + 5 + 7x + x2 Reorder the terms: 5 + 5x + -3x2 = -5 + 5 + -7x + 7x + -1x2 + x2 Combine like terms: -5 + 5 = 0 5 + 5x + -3x2 = 0 + -7x + 7x + -1x2 + x2 5 + 5x + -3x2 = -7x + 7x + -1x2 + x2 Combine like terms: -7x + 7x = 0 5 + 5x + -3x2 = 0 + -1x2 + x2 5 + 5x + -3x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 5 + 5x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1.666666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1.666666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 1.666666667 -1.666666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1.666666667x + x2 = 1.666666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 1.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 1.666666667 + 0.6944444447 Combine like terms: 1.666666667 + 0.6944444447 = 2.3611111117 0.6944444447 + -1.666666667x + x2 = 2.3611111117 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 2.3611111117 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.536590743 and -1.536590743.Subproblem 1
x + -0.8333333335 = 1.536590743 Simplifying x + -0.8333333335 = 1.536590743 Reorder the terms: -0.8333333335 + x = 1.536590743 Solving -0.8333333335 + x = 1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.536590743 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.536590743 + 0.8333333335 x = 1.536590743 + 0.8333333335 Combine like terms: 1.536590743 + 0.8333333335 = 2.3699240765 x = 2.3699240765 Simplifying x = 2.3699240765Subproblem 2
x + -0.8333333335 = -1.536590743 Simplifying x + -0.8333333335 = -1.536590743 Reorder the terms: -0.8333333335 + x = -1.536590743 Solving -0.8333333335 + x = -1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.536590743 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.536590743 + 0.8333333335 x = -1.536590743 + 0.8333333335 Combine like terms: -1.536590743 + 0.8333333335 = -0.7032574095 x = -0.7032574095 Simplifying x = -0.7032574095Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3699240765, -0.7032574095}
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