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Simplifying 4x(3x + -8) = 25 Reorder the terms: 4x(-8 + 3x) = 25 (-8 * 4x + 3x * 4x) = 25 (-32x + 12x2) = 25 Solving -32x + 12x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -32x + 12x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -32x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.083333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '2.083333333' to each side of the equation. -2.083333333 + -2.666666667x + 2.083333333 + x2 = 0 + 2.083333333 Reorder the terms: -2.083333333 + 2.083333333 + -2.666666667x + x2 = 0 + 2.083333333 Combine like terms: -2.083333333 + 2.083333333 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 2.083333333 -2.666666667x + x2 = 0 + 2.083333333 Combine like terms: 0 + 2.083333333 = 2.083333333 -2.666666667x + x2 = 2.083333333 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 = 2.083333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 2.083333333 + 1.777777780 Combine like terms: 2.083333333 + 1.777777780 = 3.861111113 1.777777780 + -2.666666667x + x2 = 3.861111113 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 3.861111113 Calculate the square root of the right side: 1.964971021 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.964971021 and -1.964971021.Subproblem 1
x + -1.333333334 = 1.964971021 Simplifying x + -1.333333334 = 1.964971021 Reorder the terms: -1.333333334 + x = 1.964971021 Solving -1.333333334 + x = 1.964971021 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 = 1.964971021 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.964971021 + 1.333333334 x = 1.964971021 + 1.333333334 Combine like terms: 1.964971021 + 1.333333334 = 3.298304355 x = 3.298304355 Simplifying x = 3.298304355Subproblem 2
x + -1.333333334 = -1.964971021 Simplifying x + -1.333333334 = -1.964971021 Reorder the terms: -1.333333334 + x = -1.964971021 Solving -1.333333334 + x = -1.964971021 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 = -1.964971021 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.964971021 + 1.333333334 x = -1.964971021 + 1.333333334 Combine like terms: -1.964971021 + 1.333333334 = -0.631637687 x = -0.631637687 Simplifying x = -0.631637687Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.298304355, -0.631637687}
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