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Simplifying -3 + 9x(x + -4) = 16x + 4 + -7x Reorder the terms: -3 + 9x(-4 + x) = 16x + 4 + -7x -3 + (-4 * 9x + x * 9x) = 16x + 4 + -7x -3 + (-36x + 9x2) = 16x + 4 + -7x Reorder the terms: -3 + -36x + 9x2 = 4 + 16x + -7x Combine like terms: 16x + -7x = 9x -3 + -36x + 9x2 = 4 + 9x Solving -3 + -36x + 9x2 = 4 + 9x Solving for variable 'x'. Reorder the terms: -3 + -4 + -36x + -9x + 9x2 = 4 + 9x + -4 + -9x Combine like terms: -3 + -4 = -7 -7 + -36x + -9x + 9x2 = 4 + 9x + -4 + -9x Combine like terms: -36x + -9x = -45x -7 + -45x + 9x2 = 4 + 9x + -4 + -9x Reorder the terms: -7 + -45x + 9x2 = 4 + -4 + 9x + -9x Combine like terms: 4 + -4 = 0 -7 + -45x + 9x2 = 0 + 9x + -9x -7 + -45x + 9x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -7 + -45x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + -5x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -5x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -5x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + 0.7777777778 -5x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -5x + x2 = 0.7777777778 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.7777777778 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.7777777778 + 6.25 Combine like terms: 0.7777777778 + 6.25 = 7.0277777778 6.25 + -5x + x2 = 7.0277777778 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.0277777778 Calculate the square root of the right side: 2.65099562 Break this problem into two subproblems by setting (x + -2.5) equal to 2.65099562 and -2.65099562.Subproblem 1
x + -2.5 = 2.65099562 Simplifying x + -2.5 = 2.65099562 Reorder the terms: -2.5 + x = 2.65099562 Solving -2.5 + x = 2.65099562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.65099562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.65099562 + 2.5 x = 2.65099562 + 2.5 Combine like terms: 2.65099562 + 2.5 = 5.15099562 x = 5.15099562 Simplifying x = 5.15099562Subproblem 2
x + -2.5 = -2.65099562 Simplifying x + -2.5 = -2.65099562 Reorder the terms: -2.5 + x = -2.65099562 Solving -2.5 + x = -2.65099562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.65099562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.65099562 + 2.5 x = -2.65099562 + 2.5 Combine like terms: -2.65099562 + 2.5 = -0.15099562 x = -0.15099562 Simplifying x = -0.15099562Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.15099562, -0.15099562}
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