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Simplifying -4(x + -3) * 3(x + 5) = 25 Reorder the terms: -4(-3 + x) * 3(x + 5) = 25 Reorder the terms: -4(-3 + x) * 3(5 + x) = 25 Reorder the terms for easier multiplication: -4 * 3(-3 + x)(5 + x) = 25 Multiply -4 * 3 -12(-3 + x)(5 + x) = 25 Multiply (-3 + x) * (5 + x) -12(-3(5 + x) + x(5 + x)) = 25 -12((5 * -3 + x * -3) + x(5 + x)) = 25 -12((-15 + -3x) + x(5 + x)) = 25 -12(-15 + -3x + (5 * x + x * x)) = 25 -12(-15 + -3x + (5x + x2)) = 25 Combine like terms: -3x + 5x = 2x -12(-15 + 2x + x2) = 25 (-15 * -12 + 2x * -12 + x2 * -12) = 25 (180 + -24x + -12x2) = 25 Solving 180 + -24x + -12x2 = 25 Solving for variable 'x'. Reorder the terms: 180 + -25 + -24x + -12x2 = 25 + -25 Combine like terms: 180 + -25 = 155 155 + -24x + -12x2 = 25 + -25 Combine like terms: 25 + -25 = 0 155 + -24x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -12.91666667 + 2x + x2 = 0 Move the constant term to the right: Add '12.91666667' to each side of the equation. -12.91666667 + 2x + 12.91666667 + x2 = 0 + 12.91666667 Reorder the terms: -12.91666667 + 12.91666667 + 2x + x2 = 0 + 12.91666667 Combine like terms: -12.91666667 + 12.91666667 = 0.00000000 0.00000000 + 2x + x2 = 0 + 12.91666667 2x + x2 = 0 + 12.91666667 Combine like terms: 0 + 12.91666667 = 12.91666667 2x + x2 = 12.91666667 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 12.91666667 + 1 Reorder the terms: 1 + 2x + x2 = 12.91666667 + 1 Combine like terms: 12.91666667 + 1 = 13.91666667 1 + 2x + x2 = 13.91666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 13.91666667 Calculate the square root of the right side: 3.730504881 Break this problem into two subproblems by setting (x + 1) equal to 3.730504881 and -3.730504881.Subproblem 1
x + 1 = 3.730504881 Simplifying x + 1 = 3.730504881 Reorder the terms: 1 + x = 3.730504881 Solving 1 + x = 3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.730504881 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.730504881 + -1 x = 3.730504881 + -1 Combine like terms: 3.730504881 + -1 = 2.730504881 x = 2.730504881 Simplifying x = 2.730504881Subproblem 2
x + 1 = -3.730504881 Simplifying x + 1 = -3.730504881 Reorder the terms: 1 + x = -3.730504881 Solving 1 + x = -3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.730504881 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.730504881 + -1 x = -3.730504881 + -1 Combine like terms: -3.730504881 + -1 = -4.730504881 x = -4.730504881 Simplifying x = -4.730504881Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.730504881, -4.730504881}
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