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Simplifying -4x(-2x + 6) = 9 Reorder the terms: -4x(6 + -2x) = 9 (6 * -4x + -2x * -4x) = 9 (-24x + 8x2) = 9 Solving -24x + 8x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -24x + 8x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -3x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -3x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -3x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -3x + x2 = 0 + 1.125 -3x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -3x + x2 = 1.125 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 1.125 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1.125 + 2.25 Combine like terms: 1.125 + 2.25 = 3.375 2.25 + -3x + x2 = 3.375 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 3.375 Calculate the square root of the right side: 1.837117307 Break this problem into two subproblems by setting (x + -1.5) equal to 1.837117307 and -1.837117307.Subproblem 1
x + -1.5 = 1.837117307 Simplifying x + -1.5 = 1.837117307 Reorder the terms: -1.5 + x = 1.837117307 Solving -1.5 + x = 1.837117307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.837117307 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.837117307 + 1.5 x = 1.837117307 + 1.5 Combine like terms: 1.837117307 + 1.5 = 3.337117307 x = 3.337117307 Simplifying x = 3.337117307Subproblem 2
x + -1.5 = -1.837117307 Simplifying x + -1.5 = -1.837117307 Reorder the terms: -1.5 + x = -1.837117307 Solving -1.5 + x = -1.837117307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.837117307 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.837117307 + 1.5 x = -1.837117307 + 1.5 Combine like terms: -1.837117307 + 1.5 = -0.337117307 x = -0.337117307 Simplifying x = -0.337117307Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.337117307, -0.337117307}
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