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Simplifying -4x(x + 3) = 5x + 9 Reorder the terms: -4x(3 + x) = 5x + 9 (3 * -4x + x * -4x) = 5x + 9 (-12x + -4x2) = 5x + 9 Reorder the terms: -12x + -4x2 = 9 + 5x Solving -12x + -4x2 = 9 + 5x Solving for variable 'x'. Reorder the terms: -9 + -12x + -5x + -4x2 = 9 + 5x + -9 + -5x Combine like terms: -12x + -5x = -17x -9 + -17x + -4x2 = 9 + 5x + -9 + -5x Reorder the terms: -9 + -17x + -4x2 = 9 + -9 + 5x + -5x Combine like terms: 9 + -9 = 0 -9 + -17x + -4x2 = 0 + 5x + -5x -9 + -17x + -4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -9 + -17x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 17x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 17x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 17x + 4x2 = 0 Solving 9 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 4.25x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 4.25x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 4.25x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 4.25x + x2 = 0 + -2.25 4.25x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 4.25x + x2 = -2.25 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = -2.25 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = -2.25 + 4.515625 Combine like terms: -2.25 + 4.515625 = 2.265625 4.515625 + 4.25x + x2 = 2.265625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + 2.125) equal to 1.505199322 and -1.505199322.Subproblem 1
x + 2.125 = 1.505199322 Simplifying x + 2.125 = 1.505199322 Reorder the terms: 2.125 + x = 1.505199322 Solving 2.125 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 1.505199322 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 1.505199322 + -2.125 x = 1.505199322 + -2.125 Combine like terms: 1.505199322 + -2.125 = -0.619800678 x = -0.619800678 Simplifying x = -0.619800678Subproblem 2
x + 2.125 = -1.505199322 Simplifying x + 2.125 = -1.505199322 Reorder the terms: 2.125 + x = -1.505199322 Solving 2.125 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -1.505199322 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -1.505199322 + -2.125 x = -1.505199322 + -2.125 Combine like terms: -1.505199322 + -2.125 = -3.630199322 x = -3.630199322 Simplifying x = -3.630199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.619800678, -3.630199322}Solution
x = {-0.619800678, -3.630199322}
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