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Simplifying x = (-2x + -3)(3x + -7) Reorder the terms: x = (-3 + -2x)(3x + -7) Reorder the terms: x = (-3 + -2x)(-7 + 3x) Multiply (-3 + -2x) * (-7 + 3x) x = (-3(-7 + 3x) + -2x * (-7 + 3x)) x = ((-7 * -3 + 3x * -3) + -2x * (-7 + 3x)) x = ((21 + -9x) + -2x * (-7 + 3x)) x = (21 + -9x + (-7 * -2x + 3x * -2x)) x = (21 + -9x + (14x + -6x2)) Combine like terms: -9x + 14x = 5x x = (21 + 5x + -6x2) Solving x = 21 + 5x + -6x2 Solving for variable 'x'. Reorder the terms: -21 + x + -5x + 6x2 = 21 + 5x + -6x2 + -21 + -5x + 6x2 Combine like terms: x + -5x = -4x -21 + -4x + 6x2 = 21 + 5x + -6x2 + -21 + -5x + 6x2 Reorder the terms: -21 + -4x + 6x2 = 21 + -21 + 5x + -5x + -6x2 + 6x2 Combine like terms: 21 + -21 = 0 -21 + -4x + 6x2 = 0 + 5x + -5x + -6x2 + 6x2 -21 + -4x + 6x2 = 5x + -5x + -6x2 + 6x2 Combine like terms: 5x + -5x = 0 -21 + -4x + 6x2 = 0 + -6x2 + 6x2 -21 + -4x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -21 + -4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.5 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.6666666667x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.6666666667x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.6666666667x + x2 = 0 + 3.5 -0.6666666667x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.6666666667x + x2 = 3.5 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 3.5 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 3.5 + 0.1111111112 Combine like terms: 3.5 + 0.1111111112 = 3.6111111112 0.1111111112 + -0.6666666667x + x2 = 3.6111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 3.6111111112 Calculate the square root of the right side: 1.900292375 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 1.900292375 and -1.900292375.Subproblem 1
x + -0.3333333334 = 1.900292375 Simplifying x + -0.3333333334 = 1.900292375 Reorder the terms: -0.3333333334 + x = 1.900292375 Solving -0.3333333334 + x = 1.900292375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 1.900292375 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.900292375 + 0.3333333334 x = 1.900292375 + 0.3333333334 Combine like terms: 1.900292375 + 0.3333333334 = 2.2336257084 x = 2.2336257084 Simplifying x = 2.2336257084Subproblem 2
x + -0.3333333334 = -1.900292375 Simplifying x + -0.3333333334 = -1.900292375 Reorder the terms: -0.3333333334 + x = -1.900292375 Solving -0.3333333334 + x = -1.900292375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -1.900292375 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.900292375 + 0.3333333334 x = -1.900292375 + 0.3333333334 Combine like terms: -1.900292375 + 0.3333333334 = -1.5669590416 x = -1.5669590416 Simplifying x = -1.5669590416Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2336257084, -1.5669590416}
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