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Simplifying (-3x + 4)(-3x + 4) = 20 Reorder the terms: (4 + -3x)(-3x + 4) = 20 Reorder the terms: (4 + -3x)(4 + -3x) = 20 Multiply (4 + -3x) * (4 + -3x) (4(4 + -3x) + -3x * (4 + -3x)) = 20 ((4 * 4 + -3x * 4) + -3x * (4 + -3x)) = 20 ((16 + -12x) + -3x * (4 + -3x)) = 20 (16 + -12x + (4 * -3x + -3x * -3x)) = 20 (16 + -12x + (-12x + 9x2)) = 20 Combine like terms: -12x + -12x = -24x (16 + -24x + 9x2) = 20 Solving 16 + -24x + 9x2 = 20 Solving for variable 'x'. Reorder the terms: 16 + -20 + -24x + 9x2 = 20 + -20 Combine like terms: 16 + -20 = -4 -4 + -24x + 9x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -4 + -24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -2.666666667x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -2.666666667x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + 0.4444444444 -2.666666667x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -2.666666667x + x2 = 0.4444444444 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 0.4444444444 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.4444444444 + 1.777777780 Combine like terms: 0.4444444444 + 1.777777780 = 2.2222222244 1.777777780 + -2.666666667x + x2 = 2.2222222244 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 2.2222222244 Calculate the square root of the right side: 1.490711986 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.490711986 and -1.490711986.Subproblem 1
x + -1.333333334 = 1.490711986 Simplifying x + -1.333333334 = 1.490711986 Reorder the terms: -1.333333334 + x = 1.490711986 Solving -1.333333334 + x = 1.490711986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.490711986 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.490711986 + 1.333333334 x = 1.490711986 + 1.333333334 Combine like terms: 1.490711986 + 1.333333334 = 2.82404532 x = 2.82404532 Simplifying x = 2.82404532Subproblem 2
x + -1.333333334 = -1.490711986 Simplifying x + -1.333333334 = -1.490711986 Reorder the terms: -1.333333334 + x = -1.490711986 Solving -1.333333334 + x = -1.490711986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.490711986 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.490711986 + 1.333333334 x = -1.490711986 + 1.333333334 Combine like terms: -1.490711986 + 1.333333334 = -0.157378652 x = -0.157378652 Simplifying x = -0.157378652Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.82404532, -0.157378652}
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