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Simplifying -2x(-2x + 3) + 2 = 3x + 50 Reorder the terms: -2x(3 + -2x) + 2 = 3x + 50 (3 * -2x + -2x * -2x) + 2 = 3x + 50 (-6x + 4x2) + 2 = 3x + 50 Reorder the terms: 2 + -6x + 4x2 = 3x + 50 Reorder the terms: 2 + -6x + 4x2 = 50 + 3x Solving 2 + -6x + 4x2 = 50 + 3x Solving for variable 'x'. Reorder the terms: 2 + -50 + -6x + -3x + 4x2 = 50 + 3x + -50 + -3x Combine like terms: 2 + -50 = -48 -48 + -6x + -3x + 4x2 = 50 + 3x + -50 + -3x Combine like terms: -6x + -3x = -9x -48 + -9x + 4x2 = 50 + 3x + -50 + -3x Reorder the terms: -48 + -9x + 4x2 = 50 + -50 + 3x + -3x Combine like terms: 50 + -50 = 0 -48 + -9x + 4x2 = 0 + 3x + -3x -48 + -9x + 4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -48 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12 + -2.25x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -2.25x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -2.25x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2.25x + x2 = 0 + 12 -2.25x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2.25x + x2 = 12 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 12 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 12 + 1.265625 Combine like terms: 12 + 1.265625 = 13.265625 1.265625 + -2.25x + x2 = 13.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 13.265625 Calculate the square root of the right side: 3.642200571 Break this problem into two subproblems by setting (x + -1.125) equal to 3.642200571 and -3.642200571.Subproblem 1
x + -1.125 = 3.642200571 Simplifying x + -1.125 = 3.642200571 Reorder the terms: -1.125 + x = 3.642200571 Solving -1.125 + x = 3.642200571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 3.642200571 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 3.642200571 + 1.125 x = 3.642200571 + 1.125 Combine like terms: 3.642200571 + 1.125 = 4.767200571 x = 4.767200571 Simplifying x = 4.767200571Subproblem 2
x + -1.125 = -3.642200571 Simplifying x + -1.125 = -3.642200571 Reorder the terms: -1.125 + x = -3.642200571 Solving -1.125 + x = -3.642200571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -3.642200571 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -3.642200571 + 1.125 x = -3.642200571 + 1.125 Combine like terms: -3.642200571 + 1.125 = -2.517200571 x = -2.517200571 Simplifying x = -2.517200571Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.767200571, -2.517200571}
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