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Simplifying (x + -0.3)(2x + -4) = 12 Reorder the terms: (-0.3 + x)(2x + -4) = 12 Reorder the terms: (-0.3 + x)(-4 + 2x) = 12 Multiply (-0.3 + x) * (-4 + 2x) (-0.3(-4 + 2x) + x(-4 + 2x)) = 12 ((-4 * -0.3 + 2x * -0.3) + x(-4 + 2x)) = 12 ((1.2 + -0.6x) + x(-4 + 2x)) = 12 (1.2 + -0.6x + (-4 * x + 2x * x)) = 12 (1.2 + -0.6x + (-4x + 2x2)) = 12 Combine like terms: -0.6x + -4x = -4.6x (1.2 + -4.6x + 2x2) = 12 Solving 1.2 + -4.6x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: 1.2 + -12 + -4.6x + 2x2 = 12 + -12 Combine like terms: 1.2 + -12 = -10.8 -10.8 + -4.6x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -10.8 + -4.6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.4 + -2.3x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -2.3x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -2.3x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -2.3x + x2 = 0 + 5.4 -2.3x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -2.3x + x2 = 5.4 The x term is -2.3x. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3x + 1.3225 + x2 = 5.4 + 1.3225 Reorder the terms: 1.3225 + -2.3x + x2 = 5.4 + 1.3225 Combine like terms: 5.4 + 1.3225 = 6.7225 1.3225 + -2.3x + x2 = 6.7225 Factor a perfect square on the left side: (x + -1.15)(x + -1.15) = 6.7225 Calculate the square root of the right side: 2.592778432 Break this problem into two subproblems by setting (x + -1.15) equal to 2.592778432 and -2.592778432.Subproblem 1
x + -1.15 = 2.592778432 Simplifying x + -1.15 = 2.592778432 Reorder the terms: -1.15 + x = 2.592778432 Solving -1.15 + x = 2.592778432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = 2.592778432 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = 2.592778432 + 1.15 x = 2.592778432 + 1.15 Combine like terms: 2.592778432 + 1.15 = 3.742778432 x = 3.742778432 Simplifying x = 3.742778432Subproblem 2
x + -1.15 = -2.592778432 Simplifying x + -1.15 = -2.592778432 Reorder the terms: -1.15 + x = -2.592778432 Solving -1.15 + x = -2.592778432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = -2.592778432 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = -2.592778432 + 1.15 x = -2.592778432 + 1.15 Combine like terms: -2.592778432 + 1.15 = -1.442778432 x = -1.442778432 Simplifying x = -1.442778432Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.742778432, -1.442778432}
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