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Simplifying 3x(2x + -4) + -2 = 5x + -1(3 + -4x) Reorder the terms: 3x(-4 + 2x) + -2 = 5x + -1(3 + -4x) (-4 * 3x + 2x * 3x) + -2 = 5x + -1(3 + -4x) (-12x + 6x2) + -2 = 5x + -1(3 + -4x) Reorder the terms: -2 + -12x + 6x2 = 5x + -1(3 + -4x) -2 + -12x + 6x2 = 5x + (3 * -1 + -4x * -1) -2 + -12x + 6x2 = 5x + (-3 + 4x) Reorder the terms: -2 + -12x + 6x2 = -3 + 5x + 4x Combine like terms: 5x + 4x = 9x -2 + -12x + 6x2 = -3 + 9x Solving -2 + -12x + 6x2 = -3 + 9x Solving for variable 'x'. Reorder the terms: -2 + 3 + -12x + -9x + 6x2 = -3 + 9x + 3 + -9x Combine like terms: -2 + 3 = 1 1 + -12x + -9x + 6x2 = -3 + 9x + 3 + -9x Combine like terms: -12x + -9x = -21x 1 + -21x + 6x2 = -3 + 9x + 3 + -9x Reorder the terms: 1 + -21x + 6x2 = -3 + 3 + 9x + -9x Combine like terms: -3 + 3 = 0 1 + -21x + 6x2 = 0 + 9x + -9x 1 + -21x + 6x2 = 9x + -9x Combine like terms: 9x + -9x = 0 1 + -21x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -3.5x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -3.5x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -3.5x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -3.5x + x2 = 0 + -0.1666666667 -3.5x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -3.5x + x2 = -0.1666666667 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -0.1666666667 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.1666666667 + 3.0625 Combine like terms: -0.1666666667 + 3.0625 = 2.8958333333 3.0625 + -3.5x + x2 = 2.8958333333 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.8958333333 Calculate the square root of the right side: 1.701714821 Break this problem into two subproblems by setting (x + -1.75) equal to 1.701714821 and -1.701714821.Subproblem 1
x + -1.75 = 1.701714821 Simplifying x + -1.75 = 1.701714821 Reorder the terms: -1.75 + x = 1.701714821 Solving -1.75 + x = 1.701714821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.701714821 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.701714821 + 1.75 x = 1.701714821 + 1.75 Combine like terms: 1.701714821 + 1.75 = 3.451714821 x = 3.451714821 Simplifying x = 3.451714821Subproblem 2
x + -1.75 = -1.701714821 Simplifying x + -1.75 = -1.701714821 Reorder the terms: -1.75 + x = -1.701714821 Solving -1.75 + x = -1.701714821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.701714821 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.701714821 + 1.75 x = -1.701714821 + 1.75 Combine like terms: -1.701714821 + 1.75 = 0.048285179 x = 0.048285179 Simplifying x = 0.048285179Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.451714821, 0.048285179}
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