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Simplifying 4x(3x + -5) = 7(2x + 3) Reorder the terms: 4x(-5 + 3x) = 7(2x + 3) (-5 * 4x + 3x * 4x) = 7(2x + 3) (-20x + 12x2) = 7(2x + 3) Reorder the terms: -20x + 12x2 = 7(3 + 2x) -20x + 12x2 = (3 * 7 + 2x * 7) -20x + 12x2 = (21 + 14x) Solving -20x + 12x2 = 21 + 14x Solving for variable 'x'. Reorder the terms: -21 + -20x + -14x + 12x2 = 21 + 14x + -21 + -14x Combine like terms: -20x + -14x = -34x -21 + -34x + 12x2 = 21 + 14x + -21 + -14x Reorder the terms: -21 + -34x + 12x2 = 21 + -21 + 14x + -14x Combine like terms: 21 + -21 = 0 -21 + -34x + 12x2 = 0 + 14x + -14x -21 + -34x + 12x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -21 + -34x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.75 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -2.833333333x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -2.833333333x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -2.833333333x + x2 = 0 + 1.75 -2.833333333x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -2.833333333x + x2 = 1.75 The x term is -2.833333333x. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x + 2.006944445 + x2 = 1.75 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = 1.75 + 2.006944445 Combine like terms: 1.75 + 2.006944445 = 3.756944445 2.006944445 + -2.833333333x + x2 = 3.756944445 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 3.756944445 Calculate the square root of the right side: 1.938283892 Break this problem into two subproblems by setting (x + -1.416666667) equal to 1.938283892 and -1.938283892.Subproblem 1
x + -1.416666667 = 1.938283892 Simplifying x + -1.416666667 = 1.938283892 Reorder the terms: -1.416666667 + x = 1.938283892 Solving -1.416666667 + x = 1.938283892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = 1.938283892 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 1.938283892 + 1.416666667 x = 1.938283892 + 1.416666667 Combine like terms: 1.938283892 + 1.416666667 = 3.354950559 x = 3.354950559 Simplifying x = 3.354950559Subproblem 2
x + -1.416666667 = -1.938283892 Simplifying x + -1.416666667 = -1.938283892 Reorder the terms: -1.416666667 + x = -1.938283892 Solving -1.416666667 + x = -1.938283892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = -1.938283892 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -1.938283892 + 1.416666667 x = -1.938283892 + 1.416666667 Combine like terms: -1.938283892 + 1.416666667 = -0.521617225 x = -0.521617225 Simplifying x = -0.521617225Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.354950559, -0.521617225}
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