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Simplifying (x + -1)(x + 3) + -1(-4x + -4)(x + -7) = 0 Reorder the terms: (-1 + x)(x + 3) + -1(-4x + -4)(x + -7) = 0 Reorder the terms: (-1 + x)(3 + x) + -1(-4x + -4)(x + -7) = 0 Multiply (-1 + x) * (3 + x) (-1(3 + x) + x(3 + x)) + -1(-4x + -4)(x + -7) = 0 ((3 * -1 + x * -1) + x(3 + x)) + -1(-4x + -4)(x + -7) = 0 ((-3 + -1x) + x(3 + x)) + -1(-4x + -4)(x + -7) = 0 (-3 + -1x + (3 * x + x * x)) + -1(-4x + -4)(x + -7) = 0 (-3 + -1x + (3x + x2)) + -1(-4x + -4)(x + -7) = 0 Combine like terms: -1x + 3x = 2x (-3 + 2x + x2) + -1(-4x + -4)(x + -7) = 0 Reorder the terms: -3 + 2x + x2 + -1(-4 + -4x)(x + -7) = 0 Reorder the terms: -3 + 2x + x2 + -1(-4 + -4x)(-7 + x) = 0 Multiply (-4 + -4x) * (-7 + x) -3 + 2x + x2 + -1(-4(-7 + x) + -4x * (-7 + x)) = 0 -3 + 2x + x2 + -1((-7 * -4 + x * -4) + -4x * (-7 + x)) = 0 -3 + 2x + x2 + -1((28 + -4x) + -4x * (-7 + x)) = 0 -3 + 2x + x2 + -1(28 + -4x + (-7 * -4x + x * -4x)) = 0 -3 + 2x + x2 + -1(28 + -4x + (28x + -4x2)) = 0 Combine like terms: -4x + 28x = 24x -3 + 2x + x2 + -1(28 + 24x + -4x2) = 0 -3 + 2x + x2 + (28 * -1 + 24x * -1 + -4x2 * -1) = 0 -3 + 2x + x2 + (-28 + -24x + 4x2) = 0 Reorder the terms: -3 + -28 + 2x + -24x + x2 + 4x2 = 0 Combine like terms: -3 + -28 = -31 -31 + 2x + -24x + x2 + 4x2 = 0 Combine like terms: 2x + -24x = -22x -31 + -22x + x2 + 4x2 = 0 Combine like terms: x2 + 4x2 = 5x2 -31 + -22x + 5x2 = 0 Solving -31 + -22x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.2 + -4.4x + x2 = 0 Move the constant term to the right: Add '6.2' to each side of the equation. -6.2 + -4.4x + 6.2 + x2 = 0 + 6.2 Reorder the terms: -6.2 + 6.2 + -4.4x + x2 = 0 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + -4.4x + x2 = 0 + 6.2 -4.4x + x2 = 0 + 6.2 Combine like terms: 0 + 6.2 = 6.2 -4.4x + x2 = 6.2 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = 6.2 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 6.2 + 4.84 Combine like terms: 6.2 + 4.84 = 11.04 4.84 + -4.4x + x2 = 11.04 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 11.04 Calculate the square root of the right side: 3.322649545 Break this problem into two subproblems by setting (x + -2.2) equal to 3.322649545 and -3.322649545.Subproblem 1
x + -2.2 = 3.322649545 Simplifying x + -2.2 = 3.322649545 Reorder the terms: -2.2 + x = 3.322649545 Solving -2.2 + x = 3.322649545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 3.322649545 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 3.322649545 + 2.2 x = 3.322649545 + 2.2 Combine like terms: 3.322649545 + 2.2 = 5.522649545 x = 5.522649545 Simplifying x = 5.522649545Subproblem 2
x + -2.2 = -3.322649545 Simplifying x + -2.2 = -3.322649545 Reorder the terms: -2.2 + x = -3.322649545 Solving -2.2 + x = -3.322649545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -3.322649545 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -3.322649545 + 2.2 x = -3.322649545 + 2.2 Combine like terms: -3.322649545 + 2.2 = -1.122649545 x = -1.122649545 Simplifying x = -1.122649545Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.522649545, -1.122649545}
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